Tootfinder

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Generic properties of topological groups
M\'arton Elekes, Bogl\'arka Geh\'er, Tam\'as K\'atay, Tam\'as Keleti, Anett Kocsis, M\'at\'e P\'alfy

The algebraic structures of social organizations: the operad of cooperative games
Dylan Laplace Mermoud, Victor Roca i Lucio
https://arxiv.org/abs/2507.01969

The algebraic structures of social organizations: the operad of cooperative games
The main goal of this paper is to settle a conceptual framework for cooperative game theory in which the notion of composition/aggregation of games is the defining structure. This is done via the mathematical theory of algebraic operads: we start by endowing the collection of all cooperative games with any number of players with an operad structure, and we show that it generalises all the previous notions of sums, products and compositions of games considered by Owen, Shapley, von Neumann and M…

Reprieve for critically ill Mexican girl, 4, who could have died within days if deported under Trump order | The Independent
https://www.independent.co.uk/news/world/americas/us-politics/mexican-girl-critically-ill-deportation-trump-b2763187.html

Grafikkartenpreise sinken: Immer mehr GeForce RTX 5000 unter Nvidia-Empfehlung
Zahlreiche Grafikkarten sind seit Mai günstiger geworden. Insbesondere Nvidia-Modelle unterbieten immer häufiger die UVP.

Beans!!

Still some time to come over to TU Berlin to talk about "Fascist AI" with us.
(Elevator is broken so follow to posted signs that lead you to another elevator and then the session location)

@… I wonder if <line-numbers> would pair nicely with that one! (https://github.com/zachleat/line-numbers)

Microsoft launches a free cybersecurity program for European governments to boost defenses against AI-enhanced threats, particularly state-sponsored attacks (Supantha Mukherjee/Reuters)
https://www.reuters.com/sustainabil…

Listening to No Kings in The USA by Gangstagrass: #NoKings #Indivisible

That’s a good march you got going there, LA. https://mastodon.social/@IveyJanette/114797218550503687

A TERRIFYING night for Kyiv and the region: Russians ATTACKED with drones and missiles #shorts: https://benborges.xyz/2025/07/04/a-terrifying-night-for-kyiv.html

Bei der Suche nach einem Digitalisat eines Buchs über die Kriegsbegeisterung von Kulturschaffenden im 1. Weltkrieg und dem von ihnen geführten "Kampf der Kulturen" stattdessen auf aktuelle Kriegstreiberei und Desinformation stoßen. 😵‍💫

Me: “My eyes are itchy and puffy”
Wife: “I’ve scheduled an appointment with the coroner and local funeral home”
Me: 💀

Gater Gitmo is to filter out workers for Trumps new Slavery policy where he sells them to businesses.
He says the farmers will be "owners" in this video
Make Americans Slaves Again
https://bsky.app/profile/fetchstep.bsky.social/post/3lszigsx…

Hey look! It's $80 in the trunk of my car! aka food for today...
#food #affordability

Möchte jemand Sonntag zu Teddy Teclebrhan in Köln, Lanxess-Arena? Hätte noch ein paar Tickets, 50€ each. Be fast!

Now, as a Trot, I'm obviously not a huge Stalin fan but, still... 🤔
4% of the world population, 22% of all the prisoners in the world.

Being in the UK on holiday reminded me how much I love crumpets. Since I can’t easily find them in the states I’ll just make them myself.
So yeah, gonna make crumpets now… feel free to share any advice!
#food #baking

Wat een enorme shitshow in de TK zeg vandaag over het strafbaar stellen van illegaliteit en de hulp aan mensen zonder verblijfsrecht.
SGP heeft zich ineens gerealiseerd waar ze voor hebben gestemd en dat ze daar eigenlijk tegen zijn.
NSC wil dat de minister die het amendement ontraadde nu gaat uitleggen dat het amendement eigenlijk zo kwaad nog niet bedoeld is. Terecht doet hij dat niet. Dit is het wetsvoorstel en daar is geen woord Spaans bij. Strafbaar.

NSC voert druk op: hulp illegalen moet kunnen, 'anders hebben we een probleem'
NSC-fractievoorzitter Van Vroonhoven wil dat demissionair asielminister Van Weel "zwart op wit" op papier zet dat humanitaire hulp aan illegalen niet strafbaar wordt.

and, 50 years ago today, following the dead session at ace’s, #JerryGarcia & merl saunders in #berkeley with a mystery drummer, presumably the same as the previous show. bob menke/louis falenga audience tape:

Positive Vibes aus #Kiel - so eine forderne Kritik wünsche ich mir noch viel mehr. Diese gesunde Art der Unzufriedenheit ❤️
Der Ortsbeirat #Mettenhof scheint mit unserer Infrastrukturplanung zufrieden, aber kritisiert den Zeitplan. Mettenhofs Erschließung mit der

Now this is uncool: Today morning it rained slightly and I only did a walk instead of a cycling loop.
During the day it was amazingly great weather.
Now as I finished working I see a thunderstorm outside ... this doesn't feel fair

Heute: Reisen mit Freunden.
Das #Kundenglücklichmachungsposteinlieferungsgeräusch wird von @… Paketen begleitet.

This https://arxiv.org/abs/2405.05727 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Chen's theorem, Goldbach's conjecture and almost prime twins II
Let $N$ denote a sufficiently large even integer and $x$ denote a sufficiently large integer, we define $D_{1,2}(N)$ as the number of primes $p$ that such that $N - p$ has at most 2 prime factors. In this paper, we show that $D_{1,2}(N) \geqslant 1.9728 \frac{C(N) N}{(\log N)^2}$, which is rather near to the asymptotic constant $2$ in Hardy--Littlewood conjecture for Goldbach's conjecture. We also get similar results on twin prime problem and additive representations of integers. The proof comb…

Ahh...
Ook Yesilgöz gooit Wilders onder de bus.
Maar 'links' is ook een no-go voor haar. 🙃
@…
#politiek #wilders

I Paris drog många en lättnadens suck på torsdagsmorgonen, när de slog upp fönstren och möttes av en svalkande bris och 20 grader i luften. Men medan varmfronten drar vidare österut har en politisk debatt tagit fart om hur man ska klara framtidens värmeböljor. https://www.dn.se/varlde…

Infekterad strid om sol- och vindkraft i värmeböljans spår
Infekterad strid i Frankrike om sol- och vindkraft i värmeböljans spår

„Methodisch mag es da Unterschiede geben, doch der Trend ist stets der gleiche: Wer viel besitzt, kann sich die besten Anlageprofis leisten und dadurch höhere Renditen erwirtschaften als Normalverdiener – und wird somit fast von allein noch reicher.“ -So die SZ.
Das Schlüsselworte sind hier „quasi“ und „fast“, denn: natürlich passiert es nicht von alleine, sondern es wird dafür weltweit geschuftet, in Lohnarbeit oder sklavenähnlichen Verhältnissen. Und: Ein Großteil des Reichtums besteh…

Good morning from this cutie who started playing footsie with me

Digital sovereignty can’t be bargained away. The European Commission has tools, public support and a mandate to act on Big Tech. Trading that away for short-term calm would be a costly mistake.
https://www.politico.eu/article/digital-sovereignty-us-br…

Digital sovereignty can’t be bargained away
The European Commission has tools, public support and a mandate to act on Big Tech. Trading that away for short-term calm would be a costly mistake.

Dimension theory for the asymptotic couple of the field of logarithmic transseries
Allen Gehret, Elliot Kaplan, Nigel Pynn-Coates
https://arxiv.org/abs/2507.01760

Dimension theory for the asymptotic couple of the field of logarithmic transseries
In this paper we completely characterize all dimension functions on all models of the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries (Dimension Theorem). This is done by characterizing the "small" $1$-variable definable sets (Small Sets Theorem). As a byproduct, we show that $T_{\log}$ is d-minimal and does not eliminate imaginaries. Separately, we provide an abstract criterion for d-minimality, which we use to observe some new examples of d-minimal expansion…

[2025-07-04 Fri (UTC), 16 new articles found for math.CO Combinatorics]
toXiv_bot_toot

#UK people! I'm planning to take a taxi from Edinburgh airport (to Stirling, so bit longer distance); any companies to avoid and/or tips? I found some websites but they all look similar so I'm just looking for some advice!

The Value of Scaffolding https://johnmdavismusic.com/2025/06/12/the-value-of-scaffolding/comment-page-1/?utm_source=dlvr.it&utm_medium=mastodon#respond

The Value of Scaffolding
Image from pexels.com I have a real problem with the blank page. I would never make it as a writer. That empty expanse of void waiting for words… I feel that here but I’m not a writer so I just bla…

"The administration’s claims to monarchical power are a real threat to America’s constitutional order. But its executive orders and policy feints are so haphazard and poorly articulated that they amount to a kind of autocratic takeover written in smudge-able crayon: terrifying, cartoonish, and vulnerable to erasure, all at once.
This is not to say that Americans should ignore Trump’s efforts to make confetti of the Constitution. Rather, when evaluating any one Trump policy, one has to keep front of mind the possibility that it simply won’t exist by the end of the week. Despite an energetic effort by some right-wing intellectuals to make Trump out to be some kind of 14-dimensional-chess player, his approach doesn’t resemble chess so much as a denial-of-service attack on a functioning government."
#USPolitcs
https://www.theatlantic.com/politics/archive/2025/06/trump-self-destructive-agenda/683013/

There's still a few things I want to improve, like maybe adding some tags and having the archival links in the feed as well, but at least it works for now!

@… @… Oh, thanks! I appreciate the recommendation.

Probably isomorphic structures
Ilijas Farah, Andrea Vaccaro
https://arxiv.org/abs/2507.01518 https://arxiv.org/pdf/2507.01518

Probably isomorphic structures
Two structures $M, N$ in the same language are called probably isomorphic if they (or, in case of metric structures, their completions) are isomorphic after forcing with the Lebesgue measure algebra. We show that, if $M$ and $N$ are discrete structures, or extremal models of a non-degenerate simplicial theory, then $M$ and $N$ are probably isomorphic if and only if $L^1([0,1], M) \cong L^1([0,1], N)$. We moreover employ some of the set-theoretic arguments used to prove the aforementioned result…

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- Higher-dimensional counterexamples to Hamiltonicity
Bruno Benedetti, Marta Pavelka

LinkedIn just sent me a warning and deleted a comment in which I called Elon Musk, who is a Nazi, a Nazi who is racist. And a Nazi.

Sensor Tower: daily US users of PDD Holdings' Temu fell by 58% in May; the US closed the "de minimis" loophole on May 2, and Temu then slashed its ad spending (Reuters)
https://www.reuters.com/business/retail-co

Russia launches another horrific attack on Kyiv hours after Trump-Putin call: https://benborges.xyz/2025/07/04/russia-launches-another-horrific-attack.html

Congress has approved the first national school voucher plan,
which will help all but the wealthiest families pay for private school and other educational expenses.
The plan, passed on Thursday as part of Republicans’ all-encompassing domestic policy bill,
now heads to the desk of President Trump, who is expected to sign it into law.
Families who earn up to 300 percent of their area’s median income, equivalent to more than $300,000 in some parts of the country,
…

Congress Passes a National School Voucher Program
The plan, part of the Republican domestic policy bill, includes all but the wealthiest families. But states must opt in, which could limit its reach.

An die Leute hier, die keine begeisterten Fahrradfaherer*innen oder auch überhaupt keine Fahrradfahrer*innen sind, mit was für Posts und Informationen könnte man euch für Fahrräder und das Fahrradfahren interessieren?

$\mathsf{MA} (\mathcal{I}$) and a Failure of Separation on the third Level
Stefan Hoffelner
https://arxiv.org/abs/2507.01187 https://…

$\mathsf{MA} (\mathcal{I}$) and a Failure of Separation on the third Level
We present a method which forces the failure of $Π^1_3$ and $Σ^1_3$-separation, while $\mathsf{MA} (\mathcal{I}$) holds, for $\mathcal{I}$ the family of indestructible ccc forcings. This shows that, in contrast to the assumption $\mathsf{BPFA}$ and $\aleph_1=\aleph_1^L$ which implies $Π^1_3$-separation, that weaker forcing axioms do not decide separation on the third projective level.

The independence and clique cover numbers of the squarefree graph
Boris Alexeev, Dustin G. Mixon, Will Sawin
https://arxiv.org/abs/2507.01928 https://

The independence and clique cover numbers of the squarefree graph
We determine the largest subset $A\subseteq \{1,\dotsc,n\}$ such that for all $a,b\in A$, the product $ab$ is not squarefree. Specifically, the maximum size is achieved by the \emph{complement} of the odd squarefree numbers. This resolves a problem of Paul Erdős and András Sárközy from 1992.

Ahh ... Soms is het wel eens handig om een wekker overdag te zetten...
... weet je gelijk hoe het komt dat je er dwars doorheen slaapt. 😂😂🙈

It's 2025. How can that ever, like _ever_ happen?
https://23.social/@thomasfricke/114625058446126352

Thomas Fricke (he/him) (@thomasfricke@23.social)
Attached: 1 image An all male panel talking about #AI discrimination. Priceless. #wiconf2025

$\text{NS}_{\omega_1}$ saturated, $\Delta_1 ( \{ \omega_1 \} )$-definable and a $\Delta^1_4$-definable well-order of the reals
Stefan Hoffelner
https://arxiv.org/abs/2507.01183

$\text{NS}_{ω_1}$ saturated, $Δ_1 ( \{ ω_1 \} )$-definable and a $Δ^1_4$-definable well-order of the reals
Assuming $M_1$, the canonical inner model with one Woodin cardinal exists, we construct a model in which the nonstationary ideal on $ω_1$ is $\aleph_2$-saturated, $Δ_1$-definable with $ω_1$ as the only parameter and there is a $Σ^1_{4}$-definable well-order of the reals. This implies that contrary to the assumption that $NS_{ω_1}$ is $\aleph_1$-dense, the assumption of $NS_{ω_1}$ being saturated and $Δ_1$-definable does not imply any nice structural properties for the projective subsets …

On the Visibility Polynomial of Graphs
Tonny K B, Shikhi M
https://arxiv.org/abs/2507.01851 https://arxiv.org/pdf/2507.01851

On the Visibility Polynomial of Graphs
Let G(V,E) be a simple graph and let X subset of V. Two vertices u and v are said to be X-visible if there exists a shortest u,v-path P such that V(P) intersection X is a subset of {u, v}. A set X is called a mutual-visibility set of G if every pair of vertices in X are X-visible. The visibility polynomial of a graph G is defined as nu (G)=sum_{i >= 0} r_i x^i, where r_i denotes the number of mutual-visibility sets in G of cardinality i. In the present paper, the visibility polynomial is studie…

Russia intensifying use of chemical weapons in Ukraine, Dutch intelligence reports: https://benborges.xyz/2025/07/04/russia-intensifying-use-of-chemical.html

China's state TV broadcaster has revealed details of a new
"graphite bomb"
that can cause a "complete loss of electricity" across an area of 10,000 square meters,
or knock out entire power stations, the South China Morning Post reported.
An animated video released by China's CCTV showed a missile being launched from a ground-based launcher
and then flying to a target where it releases 90 small submunitions.
They then bounce on t…

Video teases new Chinese blackout bomb that can knock out enemy power stations
Animation shared by state broadcaster shows what appears to be graphite bomb designed to disrupt command and control systems.

The set-theoretic Kaufmann-Clote question
Zachiri McKenzie
https://arxiv.org/abs/2507.01176 https://arxiv.org/pdf/2507.01176

The set-theoretic Kaufmann-Clote question
Let $\mathsf{M}$ be the set theory obtained from $\mathsf{ZF}$ by removing the collection scheme, restricting separation to $Δ_0$-formulae and adding an axiom asserting that every set is contained in a transitive set. Let $Π_n\textsf{-Collection}$ denote the restriction of the collection scheme to $Π_n$-formulae. In this paper we prove that for $n \geq 1$, if $\mathcal{M}$ is a model of $\mathsf{M}+Π_n\textsf{-Collection}+\mathsf{V=L}$ and $\mathcal{N}$ is a $Σ_{n+1}$-elementary end extens…

Embedding a Praeger-Xu graph into a surface
Zhaochen Ding, Zheng Guo, Luyi Liu
https://arxiv.org/abs/2507.01716 https://arxiv.org/pdf…

Embedding a Praeger-Xu graph into a surface
Rotary maps (orientably regular maps) are highly symmetric graph embeddings on orientable surfaces. This paper classifies all rotary maps whose underlying graphs are Praeger-Xu graphs, denoted $\operatorname{C}(p,r,s)$, for any odd prime $p$ that does not divide $r$. Our main result establishes a one-to-one correspondence between the isomorphism classes of these maps and the multiplicity-free representations of the dihedral group $\operatorname{D}_{2r}$ over the finite field $\mathbb{F}_p$. Thi…

Godverdomme. ...
mn huisarts:
Je hebt toch Joost die vlak bik je staat en je bij kan staan?
Ik ken helemaal geen Joost. De enige die vlak mij me stond wasn vriendin waar de gemeente de nodige streken mee uithaalde.
(En mn kinderen waar we sinds het begin van de WMO verbetering in zouden maken, maar wat nu echt verbroken is. Ook die heten geen Joost)

A Strong Kurepa Tree
John Krueger
https://arxiv.org/abs/2507.01133 https://arxiv.org/pdf/2507.01133

A Strong Kurepa Tree
We prove that it is consistent that there exists a Kurepa tree $T$ such that ${}^{ω_1}2$ is a continuous image of the topological space $[T]$ consisting of all cofinal branches of $T$ with respect to the cone topologies. This result solves an open problem due to Bergfalk, Chodounský, Guzmán, and Hrušák. We also prove that any Kurepa tree with the above property contains an Aronszajn subtree.

Some exact inducibility-type results for graphs via flag algebras
Levente Bodn\'ar, Oleg Pikhurko
https://arxiv.org/abs/2507.01596 https://

Some exact inducibility-type results for graphs via flag algebras
The $(κ,\ell)$-edge-inducibility problem asks for the maximum number of $κ$-subsets inducing exactly $\ell$ edges that a graph of given order $n$ can have. Using flag algebras and stability approach, we resolve this problem for all sufficiently large $n$ (including a description of all extremal and almost extremal graphs) in eleven new non-trivial cases when $κ\le 7$. We also compute the $F$-inducibility constant (the asymptotically maximum density of induced copies of $F$ in a graph of gi…

'There will be 1,000 units per day' — Ukrainian commander warns of increased Russian Shahed drone attacks: https://benborges.xyz/2025/07/04/there-will-be-units-per.html

[2025-07-03 Thu (UTC), 6 new articles found for math.LO Logic]
toXiv_bot_toot

Multipacking in Hypercubes
Deepak Rajendraprasad, Varun Sani, Birenjith Sasidharan, Jishnu Sen
https://arxiv.org/abs/2507.01565 https://

Multipacking in Hypercubes
For an undirected graph $G$, a dominating broadcast on $G$ is a function $f : V(G) \rightarrow \mathbb{N}$ such that for any vertex $u \in V(G)$, there exists a vertex $v \in V(G)$ with $f(v) \geqslant 1$ and $d(u,v) \leqslant f(v)$. The cost of $f$ is $\sum_{v \in V} f(v)$. The minimum cost over all the dominating broadcasts on $G$ is defined as the broadcast domination number $γ_b(G)$ of $G$. A multipacking in $G$ is a subset $M \subseteq V(G)$ such that, for every vertex $v \in V(G)$ and ev…

Wat heerlijk om niet naar het debat te kijken en wel naar oude afleveringen Star Trek...
@… #debat

Size-Ramsey numbers of tight paths
Shoham Letzter, Alexey Pokrovskiy, Liana Yepremyan
https://arxiv.org/abs/2507.01498 https://arxiv.…

Size-Ramsey numbers of tight paths
The $s$-colour size-Ramsey number of a hypergraph $H$ is the minimum number of edges in a hypergraph $G$ whose every $s$-edge-colouring contains a monochromatic copy of $H$. We show that the $s$-colour size-Ramsey number of the $r$-uniform tight path on $n$ vertices is linear in $n$, for every fixed $r$ and $s$, thereby answering a question of Dudek, La Fleur, Mubayi and Rödl (2017).

Computability of a Whitney Extension
Andrea Brun, Guido Gherardi, Alberto Marcone
https://arxiv.org/abs/2507.02113 https://arxiv.org/…

Computability of a Whitney Extension
We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if $F \subseteq \mathbb{R}^n$ is a closed set represented so that the distance function $x \mapsto d(x,F)$ can be computed, and $(f^{(\bar{k})})_{|\bar{k}| \le m}$ is a Whitney jet of order $m$ on $F$, then we can compute $g \in C^{m}(\mathbb{R}^n)$ such that $g$ and its partial derivatives coincide on $F$ with the corresponding functions of $(f^{(\bar{k})})_{|…

Spherical designs for finite quaternionic unit groups and their applications to modular forms
Masatake Hirao, Hiroshi Nozaki, Koji Tasaka
https://arxiv.org/abs/2507.01358

Spherical designs for finite quaternionic unit groups and their applications to modular forms
For a finite subset $X$ of the $d$-dimensional unit sphere, the harmonic strength $T(X)$ of $X$ is the set of $\ell\in \mathbb{N}$ such that $\sum_{x\in X} P(x)=0$ for all harmonic polynomials $P$ of homogeneous degree $\ell$. We will study three exceptional finite groups of unit quaternions, called the binary tetrahedral group $2T$ of order 24, the octahedral group $2O$ of order 48, and the icosahedral group $2I$ of order 120, which can be viewed as a subset of the 3-dimensional unit sphere. F…

[2025-07-04 Fri (UTC), 2 new articles found for math.LO Logic]
toXiv_bot_toot

Unimodality for Radon partitions of random vectors
Swee Hong Chan, Gil Kalai, Bhargav Narayanan, Natalya Ter-Saakov, Moshe White
https://arxiv.org/abs/2507.01353

Unimodality for Radon partitions of random vectors
Consider the (almost surely) unique Radon partition of a set of $n$ random Gaussian vectors in $\mathbb R^{n-2}$; choose one of the two parts of this partition uniformly at random, and for $0 \le k \le n$, let $p_k$ denote the probability that it has size $k$. In this paper, we prove strong unimodality results for the distribution $(p_0,\dots,p_n)$.

Abstract Model Structures and Compactness Theorems
Sayantan Roy, Sankha S. Basu, Mihir K. Chakraborty
https://arxiv.org/abs/2507.02343 https://

Abstract Model Structures and Compactness Theorems
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the syntactic/semantic particularities of the corresponding logic. In this paper, using the notion of \emph{abstract model structures}, we show that one can develop a generalized notion of compactness that is independent of these. Several characterization theorems f…

Permanental Analog of the Rank-Nullity Theorem for Symmetric Matrices
Priyanshu Kumar Pant, Surabhi Chakrabartty, Ranveer Singh
https://arxiv.org/abs/2507.01344

Permanental Analog of the Rank-Nullity Theorem for Symmetric Matrices
The rank-nullity theorem is a core result in the study of matrices. The rank of an $n \times n$ matrix is equal to the size of its largest square submatrix with a nonzero determinant; it can be computed in $O(n^{2.37})$ time. For symmetric matrices, the rank equals to the number of nonzero eigenvalues (that is, the nonzero roots of the characteristic polynomial), which implies that the nullity equals the multiplicity of zero eigenvalue. Similar to the rank, the permanental rank of a matrix is t…

The inverse $Z$-polynomial of a matroid
Alice L. L. Gao, Xuan Ruan, Matthew H. Y. Xie
https://arxiv.org/abs/2507.01332 https://arxiv.…

The inverse $Z$-polynomial of a matroid
Motivated by the $Z$-polynomials of matroids, Ferroni, Matherne, Stevens, and Vecchi introduced the inverse $Z$-polynomial of a matroid. In this paper, we prove several fundamental properties of the inverse $Z$-polynomial, including non-negativity and multiplicativity, and show that it is a valuative invariant. We also provide explicit formulas for the inverse $Z$-polynomials of uniform matroids and a broader class of matroids, namely sparse paving matroids, which include uniform matroids as a …

Spectral extremal problem for the odd prism
Xinhui Duan, Lu Lu
https://arxiv.org/abs/2507.01266 https://arxiv.org/pdf/2507.01266

Spectral extremal problem for the odd prism
The spectral Turán number $\spex(n, F)$ denotes the maximum spectral radius $ρ(G)$ of an $F$-free graph $G$ of order $n$. This paper determines $\spex\left(n, C_{2k+1}^{\square}\right)$ for all sufficiently large $n$, establishing the unique extremal graph. Here, $C_{2k+1}^{\square}$ is the odd prism -- the Cartesian product $C_{2k+1} \square K_2$ -- where the Cartesian product $G \square F$ has vertex set $V(G) \times V(F)$, and edges between $(u_1,v_1)$ and $(u_2,v_2)$ if either $u_1 = u_2$…

Sums along the edges of random regular graphs
Itai Benjamini, Georgii Zakharov, Maksim Zhukovskii
https://arxiv.org/abs/2507.01138 https://

Sums along the edges of random regular graphs
Let $G$ be a graph on $n$ vertices and $(H,+)$ be an abelian group. What is the minimum size ${\sf S}_H(G)$ of the set of all sums $A(u)+A(v)$ over all injections $A:V(G)\to H$? In 2012, Alon, Angel, the first author, and Lubetzky proved that, for expander graphs and $H=\mathbb{Z}$, this minimum is at least $Ω(\log n)$, and this bound is tight -- there exists a regular expander $G$ with ${\sf S}_{\mathbb{Z}}(G)=O(\log n)$. We prove that, for every constant $d\geq 3$, the random $d$-regular gra…

Cylindric growth diagrams, walks in simplices, and exclusion processes
Sergi Elizalde
https://arxiv.org/abs/2507.01097 https://arxiv.…

Cylindric growth diagrams, walks in simplices, and exclusion processes
We establish bijections between three classes of combinatorial objects that have been studied in very different contexts: lattice walks in simplicial regions as introduced by Mortimer--Prellberg, standard cylindric tableaux as introduced by Gessel--Krattenthaler and Postnikov, and sequences of states in the totally asymmetric simple exclusion process. This perspective allows us to translate symmetries from one setting into another, revealing unexpected properties of these objects. Specificall…

[2025-07-03 Thu (UTC), 13 new articles found for math.CO Combinatorics]
toXiv_bot_toot

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- A Characterization of Lines in Finite Lie Incidence Geometries of Classical Type
Sira Busch, Hendrik Van Maldeghem

The Local Structure Theorem for Graph Minors with Finite Index
Christophe Paul, Evangelos Protopapas, Dimitrios M. Thilikos, Sebastian Wiederrecht
https://arxiv.org/abs/2507.02769

The Local Structure Theorem for Graph Minors with Finite Index
The Local Structure Theorem (LST) for graph minors roughly states that every $H$-minor free graph $G$ that contains a sufficiently large wall $W$, there is a set of few vertices $A$ such that, upon removing $A$, the resulting graph $G':=G - A$ admits an "almost embedding" $δ$ into a surface $Σ$ in which $H$ does not embed. By almost embedding, we mean that there exists a hypergraph $\mathcal{H}$ whose vertex set is a subset of the vertex set of $G$ and an embedding of $\mathcal{H}$ in $Σ$ su…

A note on maximal plane subgraphs of the complete twisted graph containing perfect matchings
Elsa Oma\~na-Pulido, Eduardo Rivera-Campo
https://arxiv.org/abs/2507.02711

A note on maximal plane subgraphs of the complete twisted graph containing perfect matchings
The twisted graph $T_{n}$ is a drawing of the complete graph with $n$ vertices $v_{1},v_{2},\ldots ,v_{n}$ in which two edges $v_{i}v_{j}$ ($i

The pure condition for incidence geometries
Daniel Irving Bernstein, Signe Lundqvist
https://arxiv.org/abs/2507.02661 https://arxiv.o…

The pure condition for incidence geometries
The space of \emph{parallel redrawings} of an incidence geometry $(P,H,I)$ with an assigned set of normals is the set of points and hyperplanes in $\mathbb{R}^d$ satisfying the incidences given by $(P,H,I)$, such that the hyperplanes have the assigned normals. In 1989, Whiteley characterized the incidence geometries that have d-dimensional realizations with generic hyperplane normals such that all points and hyperplanes are distinct. However, some incidence geometries can be realized as point…

The ordering of hypertrees and unicyclic hypergraphs by the traces of $\mathcal{A}_{\alpha}$-tensor
Jueru Liu, Lizhu Sun, Changjiang Bu
https://arxiv.org/abs/2507.02650

The ordering of hypertrees and unicyclic hypergraphs by the traces of $\mathcal{A}_α$-tensor
For a real number $α\in[0,1]$ and a $k$-uniform hypergraph $\mathcal{H}$, $\mathcal{A}_α(\mathcal{H})=α\mathcal{D}(\mathcal{H})+(1-α)\mathcal{A}(\mathcal{H})$ is called the $\mathcal{A}_α$-tensor of $\mathcal{H}$, where $\mathcal{D}(\mathcal{H})$ and $\mathcal{A}(\mathcal{H})$ are the degree tensor and adjacency tensor of $\mathcal{H}$, respectively. The sum of the $d$-th powers of all eigenvalues of $\mathcal{A}_α(\mathcal{H})$ is called the $d$-th order $\mathcal{A}_α$-spectral moment …

Semisimple algebras related to immaculate tableaux
John M. Campbell
https://arxiv.org/abs/2507.02539 https://arxiv.org/pdf/2507.02539…

Semisimple algebras related to immaculate tableaux
Given a direct sum $A$ of full matrix algebras, if there is a combinatorial interpretation associated with both the dimension of $A$ and the dimensions of the irreducible $A$-modules, then this can be thought of as providing an analogue of the famous Frobenius-Young identity $n! = \sum_{λ\vdash n} ( f^λ )^{2}$ derived from the semisimple structure of the symmetric group algebra $\mathbb{C}S_{n}$, letting $f^λ$ denote the number of Young tableaux of partition shape $λ\vdash n$. By letting $g…

New orientable sequences
Chris J Mitchell, Peter R Wild
https://arxiv.org/abs/2507.02526 https://arxiv.org/pdf/2507.02526

New orientable sequences
Orientable sequences of order n are infinite periodic sequences with symbols drawn from a finite alphabet of size k with the property that any particular subsequence of length n occurs at most once in a period in either direction. They were introduced in the early 1990s in the context of possible applications in position sensing. Bounds on the period of such sequences and a range of methods of construction have been devised, although apart from very small cases a significant gap remains between…

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Definable Lipschitz selections for affine-set valued maps
Adam Parusi\'nski, Armin Rainer

Vertex-transitive nut graph order-degree existence problem
Ivan Damnjanovi\'c
https://arxiv.org/abs/2507.02481 https://arxiv.org/…

Vertex-transitive nut graph order-degree existence problem
A nut graph is a nontrivial simple graph whose adjacency matrix has a simple eigenvalue zero such that the corresponding eigenvector has no zero entries. It is known that the order $n$ and degree $d$ of a vertex-transitive nut graph satisfy $4 \mid d$, $d \ge 4$, $2 \mid n$ and $n \ge d + 4$; or $d \equiv 2 \pmod 4$, $d \ge 6$, $4 \mid n$ and $n \ge d + 6$. Here, we prove that for each such $n$ and $d$, there exists a $d$-regular Cayley nut graph of order $n$. As a direct consequence, we obtain…

Method of Weighted Words on Cylindric Partitions
Burcu Barsak\c{c}{\i}
https://arxiv.org/abs/2507.02435 https://arxiv.org/pdf/2507.02…

Method of Weighted Words on Cylindric Partitions
We study the generating functions of cylindric partitions having profile $c=(c_1, c_2, \ldots, c_r)$ with rank $2$ and levels $2, 3$ and $4$. As a result, we give expressions alternative to Borodin's formula for these generating functions. We use the method of weighted words which was first introduced by Alladi and Gordon, later was applied by Dousse in a new version to prove some partition identities and to get infinite products. We adopt the method to our subject with a more combinatorial app…

Refinements of provability and consistency principles for the second incompleteness theorem
Taishi Kurahashi
https://arxiv.org/abs/2507.00955 https://

Refinements of provability and consistency principles for the second incompleteness theorem
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of the present paper, we show that the set $\{\mathbf{E},\mathbf{C}, \mathbf{D3}\}$ suffices to establish the unprovability of the consistency statement $\neg\, \mathrm{Pr}_T(\ulcorner 0=1 \urcorner)$. We also prove that the set $\{\mathbf{E}^{\mathrm{U}}, \math…

Characterizing circle graphs with binomial partial Petrial polynomials
Ruiqing Feng, Qi Yan, Xuan Zheng
https://arxiv.org/abs/2507.02421 https://

Characterizing circle graphs with binomial partial Petrial polynomials
The partial Petrial polynomial was first introduced by Gross, Mansour, and Tucker as a generating function that enumerates the Euler genera of all possible partial Petrials on a ribbon graph. Yan and Li later extended this polynomial invariant to circle graphs by utilizing the correspondence between circle graphs and bouquets. Their explicit computation demonstrated that paths produce binomial polynomials, specifically those containing exactly two non-zero terms. This discovery led them to pose…

On the (in)equivalence of Brouwer's fixed point theorem and Sperner's lemma
Junichi Minagawa
https://arxiv.org/abs/2507.02366 https://

On the (in)equivalence of Brouwer's fixed point theorem and Sperner's lemma
We consider Brouwer's fixed point theorem and Sperner's lemma in one dimension. We present a proof of the Brouwer theorem using the Sperner lemma, and vice versa. However, we also show that they are not equivalent, because the Sperner lemma holds in the ordered field of rational numbers, whereas proving the Brouwer theorem requires the property of completeness.

[2025-07-02 Wed (UTC), 1 new article found for math.LO Logic]
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Oriented Diameter of Mixed Graphs with Given Maximum Undirected Degree
Ran An, Hengzhe Li, Jianbing Liu, Gaoxing Sun
https://arxiv.org/abs/2507.02277 https…

Oriented Diameter of Mixed Graphs with Given Maximum Undirected Degree
In 2018, Dankelmann, Gao, and Surmacs [J. Graph Theory, 88(1): 5--17, 2018] established sharp bounds on the oriented diameter of a bridgeless undirected graph and a bridgeless undirected bipartite graph in terms of vertex degree. In this paper, we extend these results to \emph{mixed graphs}, which contain both directed and undirected edges. Let the \emph{undirected degree} $d^*_G(x)$ of a vertex $x \in V(G)$ be the number of its incident undirected edges in a mixed graph $G$ of order $n$, and…

Some Tur\'{a}n-type results for signless Laplacian spectral radius
Jian Zheng, Yongtao Li, Yi-Zheng Fan
https://arxiv.org/abs/2507.02263 https://

Some Turán-type results for signless Laplacian spectral radius
Half a century ago, Bollobás and Erdős [Bull. London Math. Soc. 5 (1973)] proved that every $n$-vertex graph $G$ with $e(G)\ge (1- \frac{1}{k} + \varepsilon )\frac{n^2}{2}$ edges contains a blowup $K_{k+1}[t]$ with $t=Ω_{k,\varepsilon}(\log n)$. A well-known theorem of Nikiforov [Combin. Probab. Comput. 18 (3) (2009)] asserts that if $G$ is an $n$-vertex graph with adjacency spectral radius $λ(G)\ge (1- \frac{1}{k} + \varepsilon)n$, then $G$ contains a blowup $K_{k+1}[t]$ with $t=Ω_{k,\var…

The Cycle Counts of Graphs
Ryan McCulloch, Brendan D. McKay, Alireza Salahshoori, Thomas Zaslavsky
https://arxiv.org/abs/2507.02260 https://

The Cycle Counts of Graphs
We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the sole additional exception 13.

Fundamental and homogeneous bases of Hopf algebras built from nonsymmetric operads
Samuele Giraudo
https://arxiv.org/abs/2507.02165 https://

Fundamental and homogeneous bases of Hopf algebras built from nonsymmetric operads
We introduce new partial order structures on the underlying sets of free nonsymmetric operads. These posets involve decorated ordered rooted trees, and their terminal intervals are lattices. These lattices are not graded, not self-dual, and not semi-distributive, but they are EL-shellable, and their Mbius functions take values in $\{-1, 0, 1\}$. They admit sublattices on the families of $m$-Fuss-Catalan objects and of forests of trees. This latter order structure is used to construct two new ba…

Marcello's completion of graphs
Johan Kok
https://arxiv.org/abs/2507.02015 https://arxiv.org/pdf/2507.02015

Marcello's completion of graphs
This paper initiates a study on a new optimization problem with regards to graph completion. The defined procedure is called, \emph{Marcello's completion} of a graph. For graph $G$ of order $n$ the \emph{Marcello number} is obtained by iteratively constructing graphs, $G_1,G_2,\dots,G_k$ by adding a maximal number of edges between pairs of distinct, non-adjacent vertices in accordance with the \emph{Marcello rule}. If for smallest $k$ the resultant graph $G_k \cong K_n$ then the Marcello number…

A tableaux formula for $q$-rook numbers
Tirtharaj Basu, Aritra Bhattacharya
https://arxiv.org/abs/2507.00766 https://arxiv.org/pdf/25…

A tableaux formula for $q$-rook numbers
We provide a formula for the Garsia-Remmel $q$-rook numbers as a sum over standard Young tableaux. We connect our formula with the coefficients in $q$-Whittaker expansion of unicellular LLT functions.

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- Applications of rational difference equations to spectral graph theory: expanded version
Elismar R. Oliveira, Vilmar Trevisan

Seeing is not believing in limited visibility cops and robbers
Bojan Ba\v{s}i\'c, Alfie Davies, Aleksa D\v{z}uklevski, Strahinja Gvozdi\'c, Yannick Mogge
https://arxiv.org/abs/2507.00941

Seeing is not believing in limited visibility cops and robbers
We consider the model of limited visibility Cops and Robbers, where the cops can only see within their $l$-neighbourhood. We prove that the number of cops needed to see the robber can be arbitrarily smaller than the number needed to capture the robber, answering an open question from the literature. We then consider how close we can get to seeing the robber when we do not have enough cops, along with a probabilistic interpretation.

Cubic torus obstructions of small Betti number
Marie Kramer
https://arxiv.org/abs/2507.00876 https://arxiv.org/pdf/2507.00876

Cubic torus obstructions of small Betti number
The embeddability of graphs into surfaces has been studied for nearly a century. While the complete set of topological obstructions is known for the sphere and the real projective plane, there are only partial results for the torus. Here we present a theoretical classification of cubic torus obstructions with Betti number at most eight.

On the association scheme of perfect matchings and their designs
John Bamberg, Lukas Klawuhn
https://arxiv.org/abs/2507.00813 https://

On the association scheme of perfect matchings and their designs
We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph $K_{2n}$. We show that they are special subsets of the association scheme obtained from the Gelfand pair $(S_{2n},S_2 \wr S_n)$. This unifies and extends results by Cameron (1976) and gives rise to new existence and non-existence results. Our methods involve working in the group algebra $\mathbb{C}[S_{2n}]$ and using the representation theory of $S_{2n}$.

Tur\'{a}n density of tight cycles minus one edge in the $\ell_2$-norm
Levente Bodn\'ar, Jinghua Deng, Jianfeng Hou, Xizhi Liu, Hongbin Zhao
https://arxiv.org/abs/2507.00812

Turán density of tight cycles minus one edge in the $\ell_2$-norm
The $3$-uniform tight $\ell$-cycle minus one edge $C_{\ell}^{3-}$ is the $3$-graph on $\ell$ vertices consisting of $\ell-1$ consecutive triples in the cyclic order. We show that for every integer $\ell \ge 5$ satisfying $\ell\not\equiv 0\pmod3$, every $C_{\ell}^{3-}$-free $3$-graph whose $\ell_2$-norm, that is, the sum of codegree squares, is close to the maximum must be structurally close to the iterative blowup of a single triple. This confirms a conjecture of Balogh--Clemen--Lidický~[Surve…

Improved bound of graph energy in terms of vertex cover number
Aniruddha Samanta
https://arxiv.org/abs/2507.00798 https://arxiv.org/p…

Improved bound of graph energy in terms of vertex cover number
Let $ G $ be a simple graph with the vertex cover number $ τ$. The energy $ \mathcal{E}(G) $ of $ G $ is the sum of the absolute values of all the adjacency eigenvalues of $ G $. In this article, we establish $ \mathcal{E}(G)\geq 2τ$ for several classes of graphs. The result significantly improves the known result $ \mathcal{E}(G)\geq 2τ-2c$ for many classes of graphs, where $ c $ is the number of odd cycles.

Nondegenerate hyperplane covers of the hypercube
Lisa Sauermann, Zixuan Xu
https://arxiv.org/abs/2507.00773 https://arxiv.org/pdf/250…

Nondegenerate hyperplane covers of the hypercube
We consider collections of hyperplanes in $\mathbb{R}^n$ covering all vertices of the $n$-dimensional hypercube $\{0,1\}^n$, which satisfy the following nondegeneracy condition: For every $v\in \{0,1\}^n$ and every $i=1,\dots,n$, we demand that there is a hyperplane $H$ in the collection with $v\in H$ such that the variable $x_i$ appears with a non-zero coefficient in the hyperplane equation describing $H$. We prove that every collection $\mathcal{H}$ of hyperplanes in $\mathbb{R}^n$ covering $…

Linear rank-metric intersecting codes
Daniele Bartoli, Martino Borello, Giuseppe Marino, Martin Scotti
https://arxiv.org/abs/2507.00569 https://

Linear rank-metric intersecting codes
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecting codes in the Hamming metric. A rank-metric code is said to be intersecting if any two nonzero codewords have supports intersecting non trivially. We explore this class from both a coding-theoretic and geometric perspective, highlighting its relationship with minimal codes, MRD codes, and Hamming-metric intersecting…