arXiv: Combinatorics最新文献

Schubert Products for Permutations with Separated Descents. 具有分离下降的排列的Schubert积。

arXiv: Combinatorics Pub Date : 2021-05-04 DOI: 10.1093/imrn/rnac299

Daoji Huang

引用次数: 11

Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers 第一种形式(q,r)-Dowling数和(q,r)-Whitney-Lah数的显式公式

arXiv: Combinatorics Pub Date : 2020-12-14 DOI: 10.29020/NYBG.EJPAM.V14I1.3900

R. Corcino, Jay M. Ontolan, Maria Rowena S. Lobrigas

引用次数: 2

Tit-for-Tat Strategy as a Deformed Zero-Determinant Strategy in Repeated Games 重复博弈中以牙还牙策略的变形零行列式策略

arXiv: Combinatorics Pub Date : 2020-12-10 DOI: 10.7566/JPSJ.90.025002

M. Ueda

引用次数: 6

$lambda$-Core Distance Partitions $lambda$-Core Distance Partitions

arXiv: Combinatorics Pub Date : 2020-12-07 DOI: 10.1016/j.laa.2020.12.012.

Xandru Mifsud

引用次数: 0

An inequality for coefficients of the real-rooted polynomials 实根多项式系数的一个不等式

arXiv: Combinatorics Pub Date : 2020-12-07 DOI: 10.1016/J.JNT.2021.02.011

J. Guo

引用次数: 3

Discordant sets and ergodic Ramsey theory. 不谐和集与遍历拉姆齐理论。

arXiv: Combinatorics Pub Date : 2020-11-30 DOI: 10.2140/involve.2022.15.89

V. Bergelson, Jake Huryn, R. Raghavan

{"title":"Discordant sets and ergodic Ramsey theory.","authors":"V. Bergelson, Jake Huryn, R. Raghavan","doi":"10.2140/involve.2022.15.89","DOIUrl":"https://doi.org/10.2140/involve.2022.15.89","url":null,"abstract":"We explore the properties of non-piecewise syndetic sets with positive upper density, which we call discordant, in countable amenable (semi)groups. Sets of this kind are involved in many questions of Ramsey theory and manifest the difference in complexity between the classical van der Waerden's theorem and Szemer'edi's theorem. We generalize and unify old constructions and obtain new results about these historically interesting sets. Here is a small sample of our results. $bullet$ We connect discordant sets to recurrence in dynamical systems, and in this setting we exhibit an intimate analogy between discordant sets and nowhere dense sets having positive measure. $bullet$ We introduce a wide-ranging generalization of the squarefree numbers, producing many examples of discordant sets in $mathbb{Z}$, $mathbb{Z}^d$, and the Heisenberg group. We develop a unified method to compute densities of these discordant sets. $bullet$ We show that, for any countable abelian group $G$, any F{o}lner sequence $Phi$ in $G$, and any $c in (0, 1)$, there exists a discordant set $A subseteq G$ with $d_Phi(A) = c$. Here $d_Phi$ denotes density along $Phi$. Along the way, we draw from various corners of mathematics, including classical Ramsey theory, ergodic theory, number theory, and topological and symbolic dynamics.","PeriodicalId":8442,"journal":{"name":"arXiv: Combinatorics","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75224450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Planar binary trees in scattering amplitudes 平面二叉树的散射振幅

arXiv: Combinatorics Pub Date : 2020-11-29 DOI: 10.4171/205-1/6

Carlos R. Mafra

引用次数: 12

An orthodontia formula for Grothendieck polynomials Grothendieck多项式的正畸公式

arXiv: Combinatorics Pub Date : 2020-11-27 DOI: 10.1090/tran/8529

Karola M'esz'aros, Linus Setiabrata, Avery St. Dizier

引用次数: 2

Set-valued domino tableaux and shifted set-valued domino tableaux 集值多米诺骨牌表和移位集值多米诺骨牌表

arXiv: Combinatorics Pub Date : 2020-11-25 DOI: 10.2140/involve.2020.13.721

Florence Maas-Gari'epy, Rebecca Patrias

引用次数: 1

Simplicial homeomorphs and trace-bounded hypergraphs 单纯同纯与迹有界超图

arXiv: Combinatorics Pub Date : 2020-11-16 DOI: 10.19086/da.36647

J. Long, Bhargav P. Narayanan, Corrine Yap

{"title":"Simplicial homeomorphs and trace-bounded hypergraphs","authors":"J. Long, Bhargav P. Narayanan, Corrine Yap","doi":"10.19086/da.36647","DOIUrl":"https://doi.org/10.19086/da.36647","url":null,"abstract":"Our first main result is a uniform bound, in every dimension $k in mathbb N$, on the topological Turan numbers of $k$-dimensional simplicial complexes: for each $k in mathbb N$, there is a $lambda_k ge k^{-2k^2}$ such that for any $k$-complex $mathcal{S}$, every $k$-complex on $n ge n_0(mathcal{S})$ vertices with at least $n^{k+1 - lambda_k}$ facets contains a homeomorphic copy of $mathcal{S}$. This was previously known only in dimensions one and two, both by highly dimension-specific arguments: the existence of $lambda_1$ is a result of Mader from 1967, and the existence of $lambda_2$ was suggested by Linial in 2006 and recently proved by Keevash-Long-Narayanan-Scott. We deduce this geometric fact from a purely combinatorial result about trace-bounded hypergraphs, where an $r$-partite $r$-graph $H$ with partite classes $V_1, V_2, dots, V_r$ is said to be $d$-trace-bounded if for each $2 le i le r$, all the vertices of $V_i$ have degree at most $d$ in the trace of $H$ on $V_1 cup V_2 cup dots cup V_i$. Our second main result is the following estimate for the Turan numbers of degenerate trace-bounded hypergraphs: for all $r ge 2$ and $dinmathbb N$, there is an $alpha_{r,d} ge (5rd)^{1-r}$ such that for any $d$-trace-bounded $r$-partite $r$-graph $H$, every $r$-graph on $n ge n_0(H)$ vertices with at least $n^{r - alpha_{r,d}}$ edges contains a copy of $H$. This strengthens a result of Conlon-Fox-Sudakov from 2009 who showed that such a bound holds for $r$-partite $r$-graphs $H$ satisfying the stronger hypothesis that the vertex-degrees in all but one of its partite classes are bounded (in $H$, as opposed to in its traces).","PeriodicalId":8442,"journal":{"name":"arXiv: Combinatorics","volume":"205 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77040018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2