Annals of Combinatorics最新文献_第4页

Chainlink Polytopes and Ehrhart Equivalence 链锁多面体和艾哈特等价性

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2024-02-06 DOI: 10.1007/s00026-023-00683-x

Ezgi Kantarcı Oǧuz, Cem Yalım Özel, Mohan Ravichandran

引用次数: 0

The Maximum Number of Cliques in Graphs with Bounded Odd Circumference 有界奇数圆周图中的最大聚类数

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2024-01-24 DOI: 10.1007/s00026-023-00682-y

Zequn Lv, Ervin Győri, Zhen He, Nika Salia, Chuanqi Xiao, Xiutao Zhu

引用次数: 0

A Unified Combinatorial Treatment for Three Classical Truncated Theta Series 三种经典截断θ数列的统一组合处理方法

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2024-01-23 DOI: 10.1007/s00026-023-00684-w

Andrew Y. Z. Wang, Ang Xiao

引用次数: 0

A Succinct Proof of Defant and Kravitz’s Theorem on the Length of Hitomezashi Loops 德凡特和克拉维茨关于人字形环路长度定理的简明证明

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2024-01-02 DOI: 10.1007/s00026-023-00681-z

Qiuyu Ren, Shengtong Zhang

引用次数: 0

Two Enriched Poset Polytopes 两个丰富的 Poset 多面体

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-12-22 DOI: 10.1007/s00026-023-00679-7

Soichi Okada, Akiyoshi Tsuchiya

引用次数: 0

Approximate Sampling of Graphs with Near-P-Stable Degree Intervals 近似采样具有近 P 稳定度区间的图

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-12-21 DOI: 10.1007/s00026-023-00678-8

Péter L. Erdős, Tamás Róbert Mezei, István Miklós

{"title":"Approximate Sampling of Graphs with Near-P-Stable Degree Intervals","authors":"Péter L. Erdős, Tamás Róbert Mezei, István Miklós","doi":"10.1007/s00026-023-00678-8","DOIUrl":"10.1007/s00026-023-00678-8","url":null,"abstract":"<div>The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current result about the well-studied switch Markov chain is that it is rapidly mixing on P-stable degree sequences (see DOI:10.1016/j.ejc.2021.103421). The switch Markov chain does not change any degree sequence. However, there are cases where degree intervals are specified rather than a single degree sequence. (A natural scenario where this problem arises is in hypothesis testing on social networks that are only partially observed.) Rechner, Strowick, and Müller–Hannemann introduced in 2018 the notion of degree interval Markov chain which uses three (separately well studied) local operations (switch, hinge-flip and toggle), and employing on degree sequence realizations where any two sequences under scrutiny have very small coordinate-wise distance. Recently, Amanatidis and Kleer published a beautiful paper (DOI:10.4230/LIPIcs.STACS.2023.7), showing that the degree interval Markov chain is rapidly mixing if the sequences are coming from a system of very thin intervals which are centered not far from a regular degree sequence. In this paper, we substantially extend their result, showing that the degree interval Markov chain is rapidly mixing if the intervals are centered at P-stable degree sequences.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00678-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139017850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An Asymptotic Lower Bound on the Number of Polyominoes 多面体数量的渐近下限

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-12-21 DOI: 10.1007/s00026-023-00675-x

Vuong Bui

{"title":"An Asymptotic Lower Bound on the Number of Polyominoes","authors":"Vuong Bui","doi":"10.1007/s00026-023-00675-x","DOIUrl":"10.1007/s00026-023-00675-x","url":null,"abstract":"<div>Let P(n) be the number of polyominoes of n cells and (lambda ) be Klarner’s constant, that is, (lambda =lim _{nrightarrow infty } root n of {P(n)}). We show that there exist some positive numbers A, T, so that for every n<div><div>$$begin{aligned} P(n) ge An^{-Tlog n} lambda ^n. end{aligned}$$</div></div>This is somewhat a step toward the well-known conjecture that there exist positive (C,theta ), so that (P(n)sim Cn^{-theta }lambda ^n) for every n. In fact, if we assume another popular conjecture that (P(n)/P(n-1)) is increasing, we can get rid of (log n) to have <div><div>$$begin{aligned} P(n)ge An^{-T}lambda ^n. end{aligned}$$</div></div>Beside the above theoretical result, we also conjecture that the ratio of the number of some class of polyominoes, namely inconstructible polyominoes, over P(n) is decreasing, by observing this behavior for the available values. The conjecture opens a nice approach to bounding (lambda ) from above, since if it is the case, we can conclude that <div><div>$$begin{aligned} lambda < 4.1141, end{aligned}$$</div></div>which is quite close to the current best lower bound (lambda > 4.0025) and greatly improves the current best upper bound (lambda < 4.5252). The approach is merely analytically manipulating the known or likely properties of the function P(n), instead of giving new insights of the structure of polyominoes. The techniques can be applied to other lattice animals and self-avoiding polygons of a given area with almost no change.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139018413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Labeled Chip-Firing on Binary Trees with $$2^n-1$$ Chips 有$2^n-1$$芯片的二叉树上的标签芯片发射

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-12-15 DOI: 10.1007/s00026-023-00680-0

Gregg Musiker, Son Nguyen

引用次数: 0

The Hamilton Compression of Highly Symmetric Graphs 高度对称图的汉密尔顿压缩

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-12-13 DOI: 10.1007/s00026-023-00674-y

Petr Gregor, Arturo Merino, Torsten Mütze

{"title":"The Hamilton Compression of Highly Symmetric Graphs","authors":"Petr Gregor, Arturo Merino, Torsten Mütze","doi":"10.1007/s00026-023-00674-y","DOIUrl":"10.1007/s00026-023-00674-y","url":null,"abstract":"<div>We say that a Hamilton cycle (C=(x_1,ldots ,x_n)) in a graph G is k-symmetric, if the mapping (x_imapsto x_{i+n/k}) for all (i=1,ldots ,n), where indices are considered modulo n, is an automorphism of G. In other words, if we lay out the vertices (x_1,ldots ,x_n) equidistantly on a circle and draw the edges of G as straight lines, then the drawing of G has k-fold rotational symmetry, i.e., all information about the graph is compressed into a (360^circ /k) wedge of the drawing. The maximum k for which there exists a k-symmetric Hamilton cycle in G is referred to as the Hamilton compression of G. We investigate the Hamilton compression of four different families of vertex-transitive graphs, namely hypercubes, Johnson graphs, permutahedra and Cayley graphs of abelian groups. In several cases, we determine their Hamilton compression exactly, and in other cases, we provide close lower and upper bounds. The constructed cycles have a much higher compression than several classical Gray codes known from the literature. Our constructions also yield Gray codes for bitstrings, combinations and permutations that have few tracks and/or that are balanced.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00674-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138689490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The MacMahon q-Catalan is Convex MacMahon q-Catalan 是凸的

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-12-12 DOI: 10.1007/s00026-023-00677-9

Tewodros Amdeberhan, Stephan Wagner

引用次数: 0