Tootfinder

Ducci on $\mathbb{Z}_m^n$ and the Maximum Length for $n$ Odd
Mark L. Lewis, Shannon M. Tefft
https://arxiv.org/abs/2403.05319 https://

Ducci on $\mathbb{Z}_m^n$ and the Maximum Length for $n$ Odd
Define the Ducci function $D: \mathbb{Z}_m^n \to \mathbb{Z}_m^n$ so $D(x_1,x_2, ...,x_n)=(x_1+x_2 \;\text{mod} \; m, x_2+x_3 \; \text{mod} \; m, ..., x_n+x_1 \; \text{mod} \; m)$. In this paper, we will prove that for $n$ odd and $m=2^lm_1$ where $m_1$ is odd, then the largest the length of a tuple can be is $l$ and $K(\mathbb{Z}_m^n)=\{(x_1, x_2, ..., x_n) \in \mathbb{Z}_m^n \; \mid \; x_1+x_2+ \cdots +x_n \equiv 0 \; \text{mod} \; 2^l\}$.

On the effect of a large cloud of rigid particles on the motion of an incompressible non--Newtonian fluid
Eduard Feireisl, Arnab Roy, Arghir Zarnescu
https://arxiv.org/abs/2404.06782

On the effect of a large cloud of rigid particles on the motion of an incompressible non--Newtonian fluid
We show that the collective effect of $N$ rigid bodies $(\mathcal{S}_{n,N})_{n=1}^N$ of diameters $(r_{n,N})_{n=1}^N$ immersed in an incompressible non--Newtonian fluid is negligible in the asymptotic limit $N \to \infty$ as long as their total packing volume $\sum_{n=1}^N r_{n,N}^d$, $d=2,3$ tends to zero exponentially -- $\sum_{n=1}^N r_{n,N}^d \approx A^{-N}$ -- for a certain constant $A > 1$. The result is rather surprising and in a sharp contrast with the associated homogenization problem,…

Les ours pyrénéens n’ont pas tous hiverné, Š cause du climat
#Reporterre

Les ours pyrénéens n'ont pas tous hiverné, à cause du climat
Dans le calendrier révolutionnaire de Reporterre, le mois « lézard » (anciennement « mars ») est marqué par la sortie de leur tanière des ours des Pyrénées. Seulement, voilà : cette année, certains d’entre eux n’y ont presque pas mis les pattes. L’absence de neige et la clémence des températures étaient telles que des plantigrades ont modifié leur comportement, en boudant la période d’hivernation. Ce ralentissement du métabolisme plonge d’ordinaire les ours dans…

This https://arxiv.org/abs/2202.05507 has been replaced.
link: https://scholar.google.com/scholar?q=a

Exact values for unbalanced Zarankiewicz numbers
For positive integers $s$, $t$, $m$ and $n$, the Zarankiewicz number $Z_{s,t}(m,n)$ is defined to be the maximum number of edges in a bipartite graph with parts of sizes $m$ and $n$ that has no complete biparitite subgraph containing $s$ vertices in the part of size $m$ and $t$ vertices in the part of size $n$. A simple argument shows that, for each $t \geq 2$, $Z_{2,t}(m,n)=(t-1)\binom{m}{2}+n$ when $n \geq (t-1)\binom{m}{2}$. Here, for large $m$, we determine the exact value of $Z_{2,t}(m,n)$…

HPU Poll: N.C. Registered Voters Say Inflation and National Security Are Top Issues for D.C. (High Point University)
https://www.highpoint.edu/blog/2024/04/hpu-poll-n-c-registered-voters-say-inflation-and-national-security-are-top-issues-for-d-c/
http://www.memeorandum.com/240411/p85#a240411p85

enjoying SIGBOVIK
« In bogoceptionsort the source code for bogosort is bogosorted and then compiled, this then runs and checks if the array is sorted. If the array isn't sorted then the source code is scrambled again. The bogoception sort performs similarly to bogosort for large n but excels at smaller n and need orders of magnitudes more iterations for small n. »

This https://arxiv.org/abs/2310.16962 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on strong Erdős-Hajnal for graphs with bounded VC-minimal complexity
Inspired by Adler's idea on VC minimal theories \cite{adler2008theories}, we introduce VC-minimal complexity. We show that for any $N\in\mathbb{N}^{>0}$, there is $k_N>0$ such that for any finite bipartite graph $(X,Y;E)$ with VC-minimal complexity $< N$, there exist $X'\subseteq X$, $Y'\subseteq Y$ with $|X'|\geq k_N |X|$, $|Y'|\geq k_N |Y|$ such that $X'\times Y' \subseteq E$ or $X'\times Y'\cap E=\emptyset$.

This https://arxiv.org/abs/2310.10401 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Representations of braid groups via cyclic covers of the sphere: Zariski closure and arithmeticity
Let $d \geq 2$ and $n\geq 3$ be two natural numbers. Given any sequence $κ=(k_1,\dots,k_n) \in \mathbb{Z}^n$ such that $\gcd(k_1,\dots,k_n,d)=1$, we consider the family of Riemann surfaces obtained from the plane curves defined by $y^d=\prod_{i=1}^n(x-b_i)^{k_i}$, where $\{b_1,\dots,b_n\}$ are $n$ distinct points in $\mathbb{C}$. The monodromy of the cohomology of the fibers of this family provides us with a representation of the pure braid group $\mathrm{PB}_n$ into some symplectic group. By …

Explicit lower bound for large gaps between some consecutive primes
Keiju Sono
https://arxiv.org/abs/2404.06951 https://arxiv.org/pdf…

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…

On further questions regarding unit fractions
Yang P. Liu, Mehtaab Sawhney
https://arxiv.org/abs/2404.07113 https://arxiv.org/pdf/240…

On further questions regarding unit fractions
We prove that a subset $A\subseteq [1, N]$ with \[\sum_{n\in A}\frac{1}{n} \ge (\log N)^{4/5 + o(1)}\] contains a subset $B$ such that \[\sum_{n\in B} \frac{1}{n} = 1.\] Our techniques refine those of Croot and of Bloom. Using our refinements, we additionally consider a number of questions regarding unit fractions due to Erdős and Graham.