Annals of Combinatorics最新文献_第10页

Refined Enumeration of ({{varvec{k}}})-plane Trees and ({varvec{k}})-noncrossing Trees 改进了$${{varvec{k}}}$$ k -平面树的枚举方法 $${varvec{k}}$$

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-05-10 DOI: 10.1007/s00026-023-00642-6

Isaac Owino Okoth, Stephan Wagner

引用次数: 0

The Rank of the Sandpile Group of Random Directed Bipartite Graphs 随机有向二部图的沙堆群的秩

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-04-28 DOI: 10.1007/s00026-023-00637-3

Atal Bhargava, Jack DePascale, Jake Koenig

引用次数: 1

On Promotion and Quasi-Tangled Labelings of Posets 论姿势的推广与拟纠缠标注

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-04-20 DOI: 10.1007/s00026-023-00646-2

Eliot Hodges

{"title":"On Promotion and Quasi-Tangled Labelings of Posets","authors":"Eliot Hodges","doi":"10.1007/s00026-023-00646-2","DOIUrl":"10.1007/s00026-023-00646-2","url":null,"abstract":"<div>In 2022, Defant and Kravitz introduced extended promotion (denoted ( partial )), a map that acts on the set of labelings of a poset. Extended promotion is a generalization of Schützenberger’s promotion operator, a well-studied map that permutes the set of linear extensions of a poset. It is known that if L is a labeling of an n-element poset P, then ( partial ^{n-1}(L) ) is a linear extension. This allows us to regard ( partial ) as a sorting operator on the set of all labelings of P, where we think of the linear extensions of P as the labelings which have been sorted. The labelings requiring ( n-1 ) applications of ( partial ) to be sorted are called tangled; the labelings requiring ( n-2 ) applications are called quasi-tangled. We count the quasi-tangled labelings of a relatively large class of posets called inflated rooted trees with deflated leaves. Given an n-element poset with a unique minimal element with the property that the minimal element has exactly one parent, it follows from the aforementioned enumeration that this poset has ( 2(n-1)!-(n-2)! ) quasi-tangled labelings. Using similar methods, we outline an algorithmic approach to enumerating the labelings requiring ( n-k-1 ) applications to be sorted for any fixed ( kin {1,ldots ,n-2} ). We also make partial progress towards proving a conjecture of Defant and Kravitz on the maximum possible number of tangled labelings of an n-element poset.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 2","pages":"529 - 554"},"PeriodicalIF":0.6,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47799232","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 Properties of Certain t-Regular Partitions 某些t-正则分区的算术性质

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-04-18 DOI: 10.1007/s00026-023-00649-z

Rupam Barman, Ajit Singh, Gurinder Singh

{"title":"Arithmetic Properties of Certain t-Regular Partitions","authors":"Rupam Barman, Ajit Singh, Gurinder Singh","doi":"10.1007/s00026-023-00649-z","DOIUrl":"10.1007/s00026-023-00649-z","url":null,"abstract":"<div>For a positive integer (tge 2), let (b_{t}(n)) denote the number of t-regular partitions of a nonnegative integer n. Motivated by some recent conjectures of Keith and Zanello, we establish infinite families of congruences modulo 2 for (b_9(n)) and (b_{19}(n)). We prove some specific cases of two conjectures of Keith and Zanello on self-similarities of (b_9(n)) and (b_{19}(n)) modulo 2. For (tin {6,10,14,15,18,20,22,26,27,28}), Keith and Zanello conjectured that there are no integers (A>0) and (Bge 0) for which (b_t(An+ B)equiv 0pmod 2) for all (nge 0). We prove that, for any (tge 2) and prime (ell ), there are infinitely many arithmetic progressions (An+B) for which (sum _{n=0}^{infty }b_t(An+B)q^nnot equiv 0 pmod {ell }). Next, we obtain quantitative estimates for the distributions of (b_{6}(n), b_{10}(n)) and (b_{14}(n)) modulo 2. We further study the odd densities of certain infinite families of eta-quotients related to the 7-regular and 13-regular partition functions.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 2","pages":"439 - 457"},"PeriodicalIF":0.6,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44349370","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

Bressoud–Subbarao Type Weighted Partition Identities for a Generalized Divisor Function 广义除数函数的Bressoud–Subbarao型加权划分恒等式

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-04-17 DOI: 10.1007/s00026-023-00647-1

Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni, Bibekananda Maji

引用次数: 0

Congruence Modulo 4 for Andrews’ Even Parts Below Odd Parts Partition Function 奇部配分函数下Andrews偶部的同余模4

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-03-29 DOI: 10.1007/s00026-023-00645-3

Dandan Chen, Rong Chen

引用次数: 2

Embedding Dimensions of Simplicial Complexes on Few Vertices 少量点上简单复合体的嵌入维数

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-03-28 DOI: 10.1007/s00026-023-00644-4

Florian Frick, Mirabel Hu, Verity Scheel, Steven Simon

引用次数: 3

Strict Log-Subadditivity for Overpartition Rank 过分割秩的严格对数子可加性

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-03-24 DOI: 10.1007/s00026-023-00643-5

Helen W. J. Zhang, Ying Zhong

引用次数: 1

Dominance Regions for Rank Two Cluster Algebras 秩二簇代数的优势域

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-03-20 DOI: 10.1007/s00026-023-00636-4

Dylan Rupel, Salvatore Stella

引用次数: 0

Berkovich–Uncu Type Partition Inequalities Concerning Impermissible Sets and Perfect Power Frequencies 关于不可容许集和完全工频的Berkovich–Uncu型划分不等式

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-03-16 DOI: 10.1007/s00026-023-00638-2

Damanvir Singh Binner, Neha Gupta, Manoj Upreti

{"title":"Berkovich–Uncu Type Partition Inequalities Concerning Impermissible Sets and Perfect Power Frequencies","authors":"Damanvir Singh Binner, Neha Gupta, Manoj Upreti","doi":"10.1007/s00026-023-00638-2","DOIUrl":"10.1007/s00026-023-00638-2","url":null,"abstract":"<div>Recently, Rattan and the first author (Ann. Comb. 25 (2021) 697–728) proved a conjectured inequality of Berkovich and Uncu (Ann. Comb. 23 (2019) 263–284) concerning partitions with an impermissible part. In this article, we generalize this inequality upon considering t impermissible parts. We compare these with partitions whose certain parts appear with a frequency which is a perfect (t^{th}) power. In addition, the partitions that we study here have smallest part greater than or equal to s for some given natural number s. Our inequalities hold after a certain bound, which for given t is a polynomial in s, a major improvement over the previously known bound in the case (t=1). To prove these inequalities, our methods involve constructing injective maps between the relevant sets of partitions. The construction of these maps crucially involves concepts from analysis and calculus, such as explicit maps used to prove countability of (mathbb {N}^t), and Jensen’s inequality for convex functions, and then merge them with techniques from number theory such as Frobenius numbers, congruence classes, binary numbers and quadratic residues. We also show a connection of our results to colored partitions. Finally, we pose an open problem which seems to be related to power residues and the almost universality of diagonal ternary quadratic forms.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"27 4","pages":"833 - 855"},"PeriodicalIF":0.5,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00638-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42684461","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