发布求助
文献互助 智能选刊 最新文献

Annals of Combinatorics最新文献

筛选
英文 中文
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
{"title":"Bressoud–Subbarao Type Weighted Partition Identities for a Generalized Divisor Function","authors":"Archit Agarwal,&nbsp;Subhash Chand Bhoria,&nbsp;Pramod Eyyunni,&nbsp;Bibekananda Maji","doi":"10.1007/s00026-023-00647-1","DOIUrl":"10.1007/s00026-023-00647-1","url":null,"abstract":"<div><p>In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity of Bressoud and Subbarao starting from a <i>q</i>-series identity of Ramanujan. In the present paper, we revisit the combinatorial arguments of Bressoud and Subbarao, and derive a more general weighted partition identity. Furthermore, with the help of a fractional differential operator, we establish a few more Bressoud–Subbarao type weighted partition identities beginning from an identity of Andrews, Garvan and Liang. We also found a one-variable generalization of an identity of Uchimura related to Bell polynomials.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49518651","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
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
{"title":"Congruence Modulo 4 for Andrews’ Even Parts Below Odd Parts Partition Function","authors":"Dandan Chen,&nbsp;Rong Chen","doi":"10.1007/s00026-023-00645-3","DOIUrl":"10.1007/s00026-023-00645-3","url":null,"abstract":"<div><p>We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of <span>(overline{mathcal{E}mathcal{O}}(n))</span> and further prove that <span>(overline{mathcal{E}mathcal{O}}(n)equiv 0pmod 4)</span> for almost all <i>n</i>. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44237044","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: 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
{"title":"Embedding Dimensions of Simplicial Complexes on Few Vertices","authors":"Florian Frick,&nbsp;Mirabel Hu,&nbsp;Verity Scheel,&nbsp;Steven Simon","doi":"10.1007/s00026-023-00644-4","DOIUrl":"10.1007/s00026-023-00644-4","url":null,"abstract":"<div><p>We provide a simple characterization of simplicial complexes on few vertices that embed into the <i>d</i>-sphere. Namely, a simplicial complex on <span>(d+3)</span> vertices embeds into the <i>d</i>-sphere if and only if its non-faces do not form an intersecting family. As immediate consequences, we recover the classical van Kampen–Flores theorem and provide a topological extension of the Erdős–Ko–Rado theorem. By analogy with Fáry’s theorem for planar graphs, we show in addition that such complexes satisfy the rigidity property that continuous and linear embeddability are equivalent.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00644-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41826685","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: 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
{"title":"Strict Log-Subadditivity for Overpartition Rank","authors":"Helen W. J. Zhang,&nbsp;Ying Zhong","doi":"10.1007/s00026-023-00643-5","DOIUrl":"10.1007/s00026-023-00643-5","url":null,"abstract":"<div><p>Bessenrodt and Ono initially found the strict log-subadditivity of partition function <i>p</i>(<i>n</i>), that is, <span>(p(a+b)&lt; p(a)p(b))</span> for <span>(a,b&gt;1)</span> and <span>(a+b&gt;9)</span>. Many other important partition statistics are proved to enjoy similar properties. Lovejoy introduced the overpartition rank as an analog of Dyson’s rank for partitions from the <i>q</i>-series perspective. Let <span>({overline{N}}(a,c,n))</span> denote the number of overpartitions with rank congruent to <i>a</i> modulo <i>c</i>. Ciolan computed the asymptotic formula of <span>({overline{N}}(a,c,n))</span> and showed that <span>({overline{N}}(a, c, n) &gt; {overline{N}}(b, c, n))</span> for <span>(0le a&lt;ble lfloor frac{c}{2}rfloor )</span> and <i>n</i> large enough if <span>(cge 7)</span>. In this paper, we derive an upper bound and a lower bound of <span>({overline{N}}(a,c,n))</span> for each <span>(cge 3)</span> by using the asymptotics due to Ciolan. Consequently, we establish the strict log-subadditivity of <span>({overline{N}}(a,c,n))</span> analogous to the partition function <i>p</i>(<i>n</i>).</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46460253","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: 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
{"title":"Dominance Regions for Rank Two Cluster Algebras","authors":"Dylan Rupel,&nbsp;Salvatore Stella","doi":"10.1007/s00026-023-00636-4","DOIUrl":"10.1007/s00026-023-00636-4","url":null,"abstract":"<div><p>We study the polygons defining the dominance order on <span>({varvec{g}})</span>-vectors in cluster algebras of rank 2 as in Fig. 1.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00636-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48224641","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
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,&nbsp;Neha Gupta,&nbsp;Manoj Upreti","doi":"10.1007/s00026-023-00638-2","DOIUrl":"10.1007/s00026-023-00638-2","url":null,"abstract":"<div><p>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 <i>t</i> impermissible parts. We compare these with partitions whose certain parts appear with a frequency which is a perfect <span>(t^{th})</span> power. In addition, the partitions that we study here have smallest part greater than or equal to <i>s</i> for some given natural number <i>s</i>. Our inequalities hold after a certain bound, which for given <i>t</i> is a polynomial in <i>s</i>, a major improvement over the previously known bound in the case <span>(t=1)</span>. 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 <span>(mathbb {N}^t)</span>, 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.</p></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
Identifying Young Diagrams Among Residue Multisets 残馀多集中年轻图的识别
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2023-03-06 DOI: 10.1007/s00026-023-00641-7
Salim Rostam
{"title":"Identifying Young Diagrams Among Residue Multisets","authors":"Salim Rostam","doi":"10.1007/s00026-023-00641-7","DOIUrl":"10.1007/s00026-023-00641-7","url":null,"abstract":"<div><p>To any Young diagram we can associate the multiset of residues of all its nodes. This paper is concerned with the inverse problem: given a multiset of elements of <span>(mathbb {Z}/emathbb {Z})</span>, does it comes from a Young diagram? We give a full solution in level one and a partial answer in higher levels for Young multidiagrams, using Fayers’s notions of core block and weight of a multipartition. We apply the result in level one to study a shift operation on partitions.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00641-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44460921","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
A Non-aligning Variant of Generalized Turán Problems 广义Turán问题的一个非对齐变量
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2023-02-25 DOI: 10.1007/s00026-023-00640-8
Dániel Gerbner
{"title":"A Non-aligning Variant of Generalized Turán Problems","authors":"Dániel Gerbner","doi":"10.1007/s00026-023-00640-8","DOIUrl":"10.1007/s00026-023-00640-8","url":null,"abstract":"<div><p>In the so-called generalized Turán problems we study the largest number of copies of <i>H</i> in an <i>n</i>-vertex <i>F</i>-free graph <i>G</i>. Here we introduce a variant, where <i>F</i> is not forbidden, but we restrict how copies of <i>H</i> and <i>F</i> can be placed in <i>G</i>. More precisely, given an integer <i>n</i> and graphs <i>H</i> and <i>F</i>, what is the largest number of copies of <i>H</i> in an <i>n</i>-vertex graph such that the vertex set of that copy does not contain and is not contained in the vertex set of a copy of <i>F</i>? We solve this problem for some instances, give bounds in other instances, and we use our results to determine the generalized Turán number for some pairs of graphs.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00640-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44545476","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,&nbsp;Michael J. Schlosser,&nbsp;Meesue Yoo","doi":"10.1007/s00026-023-00639-1","DOIUrl":"10.1007/s00026-023-00639-1","url":null,"abstract":"<div><p>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 <i>q</i>-binomial coefficients with arbitrary integer values and extended the work of Loeb further by examining the arithmetic properties of the <i>q</i>-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, <i>q</i>- and elliptic binomial coefficients as well as elementary and complete homogeneous symmetric functions.</p></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
Coloring Bipartite Graphs with Semi-small List Size 具有半小列表大小的二分图的着色
IF 0.5 4区 数学
Annals of Combinatorics Pub Date : 2023-01-29 DOI: 10.1007/s00026-022-00633-z
Daniel G. Zhu
{"title":"Coloring Bipartite Graphs with Semi-small List Size","authors":"Daniel G. Zhu","doi":"10.1007/s00026-022-00633-z","DOIUrl":"10.1007/s00026-022-00633-z","url":null,"abstract":"<div><p>Recently, Alon, Cambie, and Kang introduced asymmetric list coloring of bipartite graphs, where the size of each vertex’s list depends on its part. For complete bipartite graphs, we fix the list sizes of one part and consider the resulting asymptotics, revealing an invariant quantity instrumental in determining choosability across most of the parameter space. By connecting this quantity to a simple question on independent sets of hypergraphs, we strengthen bounds when a part has list size 2. Finally, we state via our framework a conjecture on general bipartite graphs, unifying three conjectures of Alon–Cambie–Kang.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-022-00633-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41929728","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: 1
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信