Annals of Combinatorics最新文献_第7页

Long Twins in Random Words 随机词中的长双胞胎

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-05-23 DOI: 10.1007/s00026-023-00651-5

Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński

引用次数: 1

On the Subdivision Algebra for the Polytope $$mathcal {U}_{I,overline{J}}$$ 关于多项式$$mathcal的细分代数{U}_｛I，overline｛J｝｝$$

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-05-19 DOI: 10.1007/s00026-023-00650-6

Matias von Bell, Martha Yip

引用次数: 0

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

IF 0.5 4区数学

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

I. Okoth, S. 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

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":null,"pages":null},"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

Lattice Paths and Negatively Indexed Weight-Dependent Binomial Coefficients 格路径与负索引权相关二项式系数

IF 0.5 4区数学

Annals of Combinatorics Pub Date : 2023-02-21 DOI: 10.1007/s00026-023-00639-1

Josef Küstner, Michael J. Schlosser, Meesue Yoo

{"title":"Lattice Paths and Negatively Indexed Weight-Dependent Binomial Coefficients","authors":"Josef Küstner, Michael J. Schlosser, Meesue Yoo","doi":"10.1007/s00026-023-00639-1","DOIUrl":"10.1007/s00026-023-00639-1","url":null,"abstract":"<div>In 1992, Loeb (Adv Math, 91:64–74, 1992) considered a natural extension of the binomial coefficients to negative entries and gave a combinatorial interpretation in terms of hybrid sets. He showed that many of the fundamental properties of binomial coefficients continue to hold in this extended setting. Recently, Formichella and Straub (Ann Comb, 23:725–748, 2019) showed that these results can be extended to the q-binomial coefficients with arbitrary integer values and extended the work of Loeb further by examining the arithmetic properties of the q-binomial coefficients. In this paper, we give an alternative combinatorial interpretation in terms of lattice paths and consider an extension of the more general weight-dependent binomial coefficients, first defined by Schlosser (Sém Lothar Combin, 81:24, 2020), to arbitrary integer values. Remarkably, many of the results of Loeb, Formichella and Straub continue to hold in the general weighted setting. We also examine important special cases of the weight-dependent binomial coefficients, including ordinary, q- and elliptic binomial coefficients as well as elementary and complete homogeneous symmetric functions.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00639-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50501781","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