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Generalizations of leaky forcing 泄漏强迫的概括
IF 0.3
Journal of Combinatorics Pub Date : 2020-09-11 DOI: 10.4310/joc.2023.v14.n4.a1
Joseph S. Alameda, J. Kritschgau, Michael Young
{"title":"Generalizations of leaky forcing","authors":"Joseph S. Alameda, J. Kritschgau, Michael Young","doi":"10.4310/joc.2023.v14.n4.a1","DOIUrl":"https://doi.org/10.4310/joc.2023.v14.n4.a1","url":null,"abstract":"Vertex leaky forcing was recently introduced as a new variation of zero forcing in order to show how vertex leaks can disrupt the zero forcing process in a graph. An edge leak is an edge that is not allowed to be forced across during the zero forcing process. The $ell$-edge-leaky forcing number of a graph is the size of a smallest zero forcing set that can force the graph blue despite $ell$ edge leaks. This paper contains an analysis of the effect of edge leaks on the zero forcing process instead of vertex leaks. Furthermore, specified $ell$-leaky forcing is introduced. The main result is that $ell$-leaky forcing, $ell$-edge-leaky forcing, and specified $ell$-leaky forcing are equivalent. Furthermore, all of these different kinds of leaks can be mixed so that vertex leaks, edge leaks, and specified leaks are used. This mixed $ell$-leaky forcing number is also the same as the (vertex) $ell$-leaky forcing number.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"54 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90109430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Tableau stabilization and lattice paths 表稳定和点阵路径
IF 0.3
Journal of Combinatorics Pub Date : 2020-09-06 DOI: 10.4310/joc.2022.v13.n1.a5
Connor Ahlbach, Jacob David, Suho Oh, Christopher Wu
{"title":"Tableau stabilization and lattice paths","authors":"Connor Ahlbach, Jacob David, Suho Oh, Christopher Wu","doi":"10.4310/joc.2022.v13.n1.a5","DOIUrl":"https://doi.org/10.4310/joc.2022.v13.n1.a5","url":null,"abstract":"If one attaches shifted copies of a skew tableau to the right of itself and rectifies, at a certain point the copies no longer experience vertical slides, a phenomenon called tableau stabilization. While tableau stabilization was originally developed to construct the sufficiently large rectangular tableaux fixed by given powers of promotion, the purpose of this paper is to improve the original bound on tableau stabilization to the number of rows of the skew tableau. In order to prove this bound, we encode increasing subsequences as lattice paths and show that various operations on these lattice paths weakly increase the maximum combined length of the increasing subsequences.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"220 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76602508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Poset topology of $s$ weak order via SB-labelings 基于sb标记的$s$弱序的偏序拓扑
IF 0.3
Journal of Combinatorics Pub Date : 2020-09-04 DOI: 10.4310/joc.2022.v13.n3.a3
Stephen Lacina
{"title":"Poset topology of $s$ weak order via SB-labelings","authors":"Stephen Lacina","doi":"10.4310/joc.2022.v13.n3.a3","DOIUrl":"https://doi.org/10.4310/joc.2022.v13.n3.a3","url":null,"abstract":"Ceballos and Pons generalized weak order on permutations to a partial order on certain labeled trees, thereby introducing a new class of lattices called $s$-weak order. They also generalized the Tamari lattice by defining a particular sublattice of $s$-weak order called the $s$-Tamari lattice. We prove that the homotopy type of each open interval in $s$-weak order and in the $s$-Tamari lattice is either a ball or sphere. We do this by giving $s$-weak order and the $s$-Tamari lattice a type of edge labeling known as an SB-labeling. We characterize which intervals are homotopy equivalent to spheres and which are homotopy equivalent to balls; we also determine the dimension of the spheres for the intervals yielding spheres.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"36 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90382787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Eulerian central limit theorems and Carlitz identities in positive elements of classical Weyl groups 经典Weyl群正元中的欧拉中心极限定理与Carlitz恒等式
IF 0.3
Journal of Combinatorics Pub Date : 2020-05-26 DOI: 10.4310/joc.2022.v13.n3.a2
Hiranya Kishore Dey, S. Sivasubramanian
{"title":"Eulerian central limit theorems and Carlitz identities in positive elements of classical Weyl groups","authors":"Hiranya Kishore Dey, S. Sivasubramanian","doi":"10.4310/joc.2022.v13.n3.a2","DOIUrl":"https://doi.org/10.4310/joc.2022.v13.n3.a2","url":null,"abstract":"Central Limit Theorems are known for the Eulerian statistic \"descent\" (or \"excedance\") in the symmetric group $SSS_n$. Recently, Fulman, Kim, Lee and Petersen gave a Central Limit Theorem for \"descent\" over the alternating group $AAA_n$ and also gave a Carlitz identity in $AAA_n$ using descents. \u0000In this paper, we give a Central Limit Theorem in $AAA_n$ involving excedances. We extend these to the positive elements in type B and type D Coxeter groups. Boroweic and Mlotkowski enumerated type B descents over $DD_n$, the type D Coxeter group and gave similar results. We refine their results for both the positive and negative part of $DD_n$. Our results are a consequence of signed enumeration over these subsets.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"2006 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82436112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Completing partial Latin squares with two filled rows and three filled columns 完成具有两行和三列填充的部分拉丁方格
IF 0.3
Journal of Combinatorics Pub Date : 2020-05-17 DOI: 10.4310/joc.2023.v14.n1.a6
C. J. Casselgren, Herman Goransson
{"title":"Completing partial Latin squares with two filled rows and three filled columns","authors":"C. J. Casselgren, Herman Goransson","doi":"10.4310/joc.2023.v14.n1.a6","DOIUrl":"https://doi.org/10.4310/joc.2023.v14.n1.a6","url":null,"abstract":"Consider a partial Latin square $P$ where the first two rows and first three columns are completely filled, and every other cell of $P$ is empty. It has been conjectured that all such partial Latin squares of order at least $8$ are completable. Based on a technique by Kuhl and McGinn we describe a framework for completing partial Latin squares in this class. Moreover, we use our method for proving that all partial Latin squares from this family, where the intersection of the nonempty rows and columns form a Latin rectangle with three distinct symbols, is completable.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"21 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75068560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cliques with many colors in triple systems 在三重体系中有许多颜色的团
IF 0.3
Journal of Combinatorics Pub Date : 2020-05-06 DOI: 10.4310/joc.2021.v12.n4.a2
D. Mubayi, Andrew Suk
{"title":"Cliques with many colors in triple systems","authors":"D. Mubayi, Andrew Suk","doi":"10.4310/joc.2021.v12.n4.a2","DOIUrl":"https://doi.org/10.4310/joc.2021.v12.n4.a2","url":null,"abstract":"Erdős and Hajnal constructed a 4-coloring of the triples of an $N$-element set such that every $n$-element subset contains 2 triples with distinct colors, and $N$ is double exponential in $n$. Conlon, Fox and Rodl asked whether there is some integer $qge 3$ and a $q$-coloring of the triples of an $N$-element set such that every $n$-element subset has 3 triples with distinct colors, and $N$ is double exponential in $n$. We make the first nontrivial progress on this problem by providing a $q$-coloring with this property for all $qgeq 9$, where $N$ is exponential in $n^{2+cq}$ and $c>0$ is an absolute constant.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"5 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78863954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Algebraic Tools 代数工具
IF 0.3
Journal of Combinatorics Pub Date : 2020-02-19 DOI: 10.1090/text/055/03
{"title":"Algebraic Tools","authors":"","doi":"10.1090/text/055/03","DOIUrl":"https://doi.org/10.1090/text/055/03","url":null,"abstract":"","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"74 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83217708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Distributions and Combinatorial Proofs 分布与组合证明
IF 0.3
Journal of Combinatorics Pub Date : 2020-02-19 DOI: 10.1090/text/055/02
{"title":"Distributions and Combinatorial\u0000 Proofs","authors":"","doi":"10.1090/text/055/02","DOIUrl":"https://doi.org/10.1090/text/055/02","url":null,"abstract":"","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":" 6","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72381920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Partially Ordered Sets 半序集
IF 0.3
Journal of Combinatorics Pub Date : 2020-02-19 DOI: 10.1007/978-1-4612-3086-1_3
Peter Cameron
{"title":"Partially Ordered Sets","authors":"Peter Cameron","doi":"10.1007/978-1-4612-3086-1_3","DOIUrl":"https://doi.org/10.1007/978-1-4612-3086-1_3","url":null,"abstract":"","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"44 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84776228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Counting Under Equivalence 等效计数
IF 0.3
Journal of Combinatorics Pub Date : 2020-02-19 DOI: 10.1090/text/055/05
{"title":"Counting Under Equivalence","authors":"","doi":"10.1090/text/055/05","DOIUrl":"https://doi.org/10.1090/text/055/05","url":null,"abstract":"","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"30 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86009474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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