Tootfinder

🔊 #NowPlaying on KEXP's #VarietyMix
Lætitia Sadier:
🎵 Don’t Forget You’re Mine
#LætitiaSadier
https://open.spotify.com/track/2vMzXeuXwbInPyLJtfOQyV
https://laetitiasadier.bandcamp.com/track/don-t-forget-you-re-mine

This https://arxiv.org/abs/2404.06951 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Explicit lower bound for large gaps between some consecutive primes
Let $p_{n}$ denote the $n$th prime and for any fixed positive integer $k$ and $X\geq 2$, put \[ G_{k}(X):=\max _{p _{n+k}\leq X} \min \{ p_{n+1}-p_{n}, \ldots , p_{n+k}-p_{n+k-1} \}. \] Ford, Maynard and Tao proved that there exists an effective abosolute constant $c_{LG}>0$ such that \[ G_{k}(X)\geq \frac{c_{LG}}{k^{2}}\frac{\log X \log \log X \log \log \log \log X}{\log \log \log X} \] holds for any sufficiently large $X$. The main purpose of this paper is to determine the constant $c_{LG}$ a…

This https://arxiv.org/abs/2404.06598 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Extremes of generalized inversions on symmetric groups
The classical inversion statistic on symmetric groups is the sum of all indicators $\textbf{1}\{π(i) > π(j)\}$ for a random permutation $π= (π(1), \ldots, π(n))$ and the pairs $(i,j)$ with $1 \leq i < j \leq n$. The descent statistic counts all $i \in \{1, \ldots, n-1\}$ with $π(i) > π(i+1)$. The number of inversions can be generalized by restricting the indicators to pairs $(i,j)$ with $i

This https://arxiv.org/abs/1904.12500 has been replaced.
link: https://scholar.google.com/scholar?q=a

Composing dynamic programming tree-decomposition-based algorithms
Given two integers $\ell$ and $p$ as well as $\ell$ graph classes $\mathcal{H}_1,\ldots,\mathcal{H}_\ell$, the problems $\mathsf{GraphPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell,p)$, \break $\mathsf{VertPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell)$, and $\mathsf{EdgePart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell)$ ask, given graph $G$ as input, whether $V(G)$, $V(G)$, $E(G)$ respectively can be partitioned into $\ell$ sets $S_1, \ldots, S_\ell$ such that, for each $i$ between $1$ and $\ell$,…

🔊 #NowPlaying on KEXP's #AfternoonShow
Lætitia Sadier:
🎵 La Nageuse Nue
#LætitiaSadier
https://open.spotify.com/track/47orBvN9aVksNz6ttRB5rF
https://laetitiasadier.bandcamp.com/track/la-nageuse-nue

On the monogenity of totally complex pure octic fields
Istv\'an Ga\'al
https://arxiv.org/abs/2402.09293 https://arxiv.org/pdf…

On the monogenity of totally complex pure octic fields
Let $0,1\ne m\in Z$ and $α=\sqrt[8]{m}$. According to the results of I. Gaál and L. El Fadil, $α$ generates a power integral basis in $K=Q(α)$, if and only if $m$ is square-free and $m\not\equiv 1\;(\bmod\; 4)$. In the present paper we consider totally complex pure octic fields, that is the case $m<0$, with $m$ satisfiying the above property. In this case $(1,α,α^2,\ldots,α^7)$ is an integral basis. Our purpose is to investigate whether $K$ admits any other generators of power integral b…

Radio number for the Cartesian product of a tree and a complete graph
Payal Vasoya, Devsi Bantva
https://arxiv.org/abs/2404.08400 https://

Radio number for the Cartesian product of a tree and a complete graph
A radio labelling of a graph $G$ is a mapping $f : V(G) \rightarrow \{0, 1, 2,\ldots\}$ such that $|f(u)-f(v)|\geq diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u,v$ of $G$, where $diam(G)$ is the diameter of $G$ and $d(u,v)$ is the distance between $u$ and $v$ in $G$. The radio number $rn(G)$ of $G$ is the smallest integer $k$ such that $G$ admits a radio labelling $f$ with $\max\{f(v):v \in V(G)\} = k$. In this paper, we give a lower bound for the radio number of the Ca…

This https://arxiv.org/abs/2306.02721 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Alternating Parity Weak Sequencing
A subset $S$ of a group $(G,+)$ is $t$-weakly sequenceable if there is an ordering $(y_1, \ldots, y_k)$ of its elements such that the partial sums~$s_0, s_1, \ldots, s_k$, given by $s_0 = 0$ and $s_i = \sum_{j=1}^i y_j$ for $1 \leq i \leq k$, satisfy $s_i \neq s_j$ whenever and $1 \leq |i-j|\leq t$. In [10] it was proved that if the order of a group is $pe$ then all sufficiently large subsets of the non-identity elements are $t$-weakly sequenceable when $p > 3$ is prime, $e \leq 3$ …

Finite sums and finite products in $IP^{\star}$ sets
Pintu Debnath
https://arxiv.org/abs/2403.09585 https://arxiv.org/pdf/2403.09585<…

Finite sums and finite products in $IP^{\star}$ sets
In \cite{key-4}, Hindman proved that for $\mathbb{N}=C_{1}\cup C_{2}\cup\ldots\cup C_{r}$, one cell contains an $AIP$ set, which was a conjecture of Graham and Rothschild. Hindman's method was combinatorial, and an algebraic proof of the Hindman finite sum theorem is followed from \cite[Corollary 5.10]{key-5}, but it was originally due to Glazer and Galvin. In \cite[Theorem 2.6]{key-2}, V. Bergelson and Hindman proved that for any $AIP^{\star}$ set $A$ and sequence $\langle x_{n}\rangle_{n=1}^{…

Finite sums and finite products in $IP^{\star}$ sets
Pintu Debnath
https://arxiv.org/abs/2403.09585 https://arxiv.org/pdf/2403.09585<…

Finite sums and finite products in $IP^{\star}$ sets
In \cite{key-4}, Hindman proved that for $\mathbb{N}=C_{1}\cup C_{2}\cup\ldots\cup C_{r}$, one cell contains an $AIP$ set, which was a conjecture of Graham and Rothschild. Hindman's method was combinatorial, and an algebraic proof of the Hindman finite sum theorem is followed from \cite[Corollary 5.10]{key-5}, but it was originally due to Glazer and Galvin. In \cite[Theorem 2.6]{key-2}, V. Bergelson and Hindman proved that for any $AIP^{\star}$ set $A$ and sequence $\langle x_{n}\rangle_{n=1}^{…