Annals of Combinatorics最新文献_第3页

On a Generalization of a Result of Kleitman 关于Kleitman一个结果的推广

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-08-02 DOI: 10.1007/s00026-025-00777-8

Ryan R. Martin, Balázs Patkós

{"title":"On a Generalization of a Result of Kleitman","authors":"Ryan R. Martin, Balázs Patkós","doi":"10.1007/s00026-025-00777-8","DOIUrl":"10.1007/s00026-025-00777-8","url":null,"abstract":"<div>A classical result of Kleitman determines the maximum number f(n, s) of subsets in a family ({{mathcal {F}}}subseteq 2^{[n]}) of sets that do not contain distinct sets (F_1,F_2,dots ,F_s) that are pairwise disjoint in the case (nequiv 0,-1) (mod s). Katona and Nagy determined the maximum size of a family of subsets of an n-element set that does not contain (A_1,A_2,dots ,A_t,B_1,B_2,dots ,B_t) with (bigcup _{i=1}^t A_i) and (bigcup _{i=1}^t B_i) being disjoint. In this paper, we consider the problem of finding the maximum number (textrm{vex}(n,K_{stimes t})) in a family ({{mathcal {F}}}subseteq 2^{[n]}) without sets (F^1_1,dots ,F^1_t,dots ,F^s_1,dots ,F^s_t) such that (G_j=bigcup _{i=1}^tF^j_i) (j=1,2,dots ,s) are pairwise disjoint. We determine the asymptotics of (2^n-textrm{vex}(n,K_{stimes t})) if (nequiv -1) (mod s) for all t, and if (nequiv 0) (mod s), (tge 3) and show that in this latter case the asymptotics of the (t=2) subcase is different from both the (t=1) and (tge 3) subcases.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 2","pages":"397 - 413"},"PeriodicalIF":0.8,"publicationDate":"2025-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00777-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323150","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

Bessenrodt–Ono Inequalities for (ell )-Tuples of Pairwise Commuting Permutations 对交换置换元组(ell )的Bessenrodt-Ono不等式

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-07-29 DOI: 10.1007/s00026-025-00767-w

Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser

{"title":"Bessenrodt–Ono Inequalities for (ell )-Tuples of Pairwise Commuting Permutations","authors":"Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser","doi":"10.1007/s00026-025-00767-w","DOIUrl":"10.1007/s00026-025-00767-w","url":null,"abstract":"<div>Let (S_n) denote the symmetric group. We consider <div><div>$$begin{aligned} N_{ell }(n):= frac{left| textrm{Hom}left( {mathbb {Z}}^{ell },S_nright) right| }{n!} end{aligned}$$</div></div>which also counts the number of (ell )-tuples (pi =left( pi _1, ldots , pi _{ell }right) in S_n^{ell }) with (pi _i pi _j = pi _j pi _i) for (1 le i,j le ell ) scaled by n!. A recursion formula, generating function, and Euler product have been discovered by Dey, Wohlfahrt, Bryan and Fulman, and White. Let (a,b, ell ge 2.) It is known by Bringmann, Franke, and Heim, that the Bessenrodt–Ono inequality <div><div>$$begin{aligned} Delta _{a,b}^{ell }:= N_{ell }(a) , N_{ell }(b) - N_{ell }(a+b) >0 end{aligned}$$</div></div>is valid for (a,b gg 1) and by Bessenrodt and Ono that it is valid for (ell =2) and (a+b >9.) In this paper, we prove that for each pair (a, b) the sign of ({Delta _{a,b}^{ell } }_{ell }) is getting stable. In each case we provide an explicit bound. The numbers (N_{ell }left( nright) ) had been identified by Bryan and Fulman as the nth orbifold characteristics, generalizing work by Macdonald and Hirzebruch–Höfer concerning the ordinary and string-theoretic Euler characteristics of symmetric products, where (N_2(n)=p(n) ) represents the partition function.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 2","pages":"553 - 573"},"PeriodicalIF":0.8,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00767-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323792","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

Solving the n-Color Ice Model 求解n色冰模型

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-07-09 DOI: 10.1007/s00026-025-00770-1

Patrick Addona, Ethan Bockenhauer, Ben Brubaker, Michael Cauthorn, Cianan Conefrey-Shinozaki, David Donze, William Dudarov, Jessamyn Dukes, Andrew Hardt, Cindy Li, Jigang Li, Yanli Liu, Neelima Puthanveetil, Zain Qudsi, Jordan Simons, Joseph Sullivan, Autumn Young

{"title":"Solving the n-Color Ice Model","authors":"Patrick Addona, Ethan Bockenhauer, Ben Brubaker, Michael Cauthorn, Cianan Conefrey-Shinozaki, David Donze, William Dudarov, Jessamyn Dukes, Andrew Hardt, Cindy Li, Jigang Li, Yanli Liu, Neelima Puthanveetil, Zain Qudsi, Jordan Simons, Joseph Sullivan, Autumn Young","doi":"10.1007/s00026-025-00770-1","DOIUrl":"10.1007/s00026-025-00770-1","url":null,"abstract":"<div>Given an arbitrary choice of two sets of nonzero Boltzmann weights for n-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the Yang–Baxter equation. Furthermore, we provide an explicit one-dimensional parametrization of all solutions in this case. These n-color lattice models are so named because their admissible vertices have adjacent edges labeled by one of n colors with additional restrictions. The two-colored case specializes to the six-vertex model, in which case our results recover the familiar quadric condition of Baxter for solvability. The general n-color case includes important solutions to the Yang–Baxter equation like the evaluation modules for the quantum affine Lie algebra (U_q(hat{mathfrak {sl}}_n)). Finally, we demonstrate the invariance of this class of solutions under natural transformations, including those associated with Drinfeld twisting.\u0000</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 3","pages":"737 - 784"},"PeriodicalIF":0.8,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007441","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

Arithmetic and Asymptotic Properties for Some Functions Related to the Least r-Gaps of Partitions 若干与分区最小r-间隙有关的函数的算术和渐近性质

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-07-07 DOI: 10.1007/s00026-025-00772-z

Nayandeep Deka Baruah, Pranjal Talukdar

引用次数: 0

Extremal Spectral Radius of Outplanar Graphs with Forbidden Structures 具有禁止结构的外平面图的极值谱半径

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-06-28 DOI: 10.1007/s00026-025-00769-8

Wen-Huan Wang, Huan-Lei Shi, Yuan-Zheng-Fang Sun

引用次数: 0

A Trivariate Dichromate Polynomial for Digraphs 有向图的三变量重铬酸盐多项式

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-06-06 DOI: 10.1007/s00026-025-00766-x

Winfried Hochstättler, Johanna Wiehe

引用次数: 0

Induced Saturation of the Poset (2C_2) 波塞特的诱导饱和 (2C_2)

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-05-30 DOI: 10.1007/s00026-025-00764-z

Ryan R. Martin, Nick Veldt

{"title":"Induced Saturation of the Poset (2C_2)","authors":"Ryan R. Martin, Nick Veldt","doi":"10.1007/s00026-025-00764-z","DOIUrl":"10.1007/s00026-025-00764-z","url":null,"abstract":"<div>Given a set X, the power set (mathcal {P}(X)), and a finite poset ((P,le _P)), a family (mathcal {F}subseteq mathcal {P}(X)) is said to be induced-P-free if there is no injection (varphi : Prightarrow mathcal {F}) such that (varphi (p)subseteq varphi (q)) if and only if (ple _{P} q) for every (p,q in P). The family (mathcal {F}) is induced-P-saturated if it is maximal with respect to being induced-P-free. If (n=|X|), then the size of the smallest induced-P-saturated family in (mathcal {P}(X)) is denoted (textrm{sat}^*(n,P)). The poset (2C_2) is two incomparable 2-chains (the Hasse diagram is two vertex-disjoint edges) and Keszegh, Lemons, Martin, Pálvölgyi, and Patkós proved that (n+2le textrm{sat}^*(n,2C_2)le 2n) and gave one isomorphism class of an induced-(2C_2)-saturated family that achieves the upper bound. We show that the lower bound can be improved to (3n/2 + 1/2) by examining the necessary structure of a saturated family. In addition, we provide many examples of induced-(2C_2)-saturated families of size 2n in (mathcal {P}(X)) where (|X|=n).</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"77 - 90"},"PeriodicalIF":0.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562051","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

Regularity of Powers and Symbolic Powers of Edge Ideals of Cubic Circulant Graphs 三次循环图边理想的幂和符号幂的正则性

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-05-26 DOI: 10.1007/s00026-025-00765-y

Nguyen Thu Hang, My Hanh Pham, Thanh Vu

引用次数: 0

Connected Components and Non-bipartiteness of Generalized Paley Graphs 广义Paley图的连通分量与非二分性

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-05-20 DOI: 10.1007/s00026-025-00758-x

Ricardo A. Podestá, Denis E. Videla

引用次数: 0

Correction to: The Likely Maximum Size of Twin Subtrees in a Large Random Tree 修正：大型随机树中孪生子树的可能最大大小