Pub Date : 2022-02-11DOI: 10.26493/1855-3974.1753.52a
Yaokun Wu, Yinfeng Zhu
Let S be a transformation semigroup acting on a set Ω. The action of S on Ω can be naturally extended to be an action on all subsets of Ω. We say that S is `-homogeneous provided it can send A to B for any two (not necessarily distinct) `-subsets A and B of Ω. On the condition that k ≤ ` < k + ` ≤ |Ω|, we show that every `-homogeneous transformation semigroup acting on Ω must be k-homogeneous. We report other variants of this result for Boolean lattices and projective geometries. In general, any semigroup action on a poset gives rise to an automaton and we associate some sequences of integers with the phase space of this automaton. When the poset is a geometric lattice, we propose to study various possible regularity properties of these sequences, especially the so-called top-heavy property.
设S是作用于集合Ω的变换半群。S对Ω的作用可以自然地扩展为对Ω的所有子集的作用。我们说S是'齐次的前提是它可以在任意两个(不一定是不同的)情况下将A传送到B- Ω的子集A和B。在k≤' < k + '≤|Ω|的条件下，证明了作用于Ω的所有'齐次变换半群必须是k齐次的。我们报告了布尔格和射影几何的其他变体。一般情况下，任意半群作用于偏序集都会产生一个自动机，我们将一些整数序列与这个自动机的相空间联系起来。当偏序集是一个几何格时，我们提出研究这些序列的各种可能的正则性，特别是所谓的头重性。
{"title":"Top-heavy phenomena for transformations","authors":"Yaokun Wu, Yinfeng Zhu","doi":"10.26493/1855-3974.1753.52a","DOIUrl":"https://doi.org/10.26493/1855-3974.1753.52a","url":null,"abstract":"Let S be a transformation semigroup acting on a set Ω. The action of S on Ω can be naturally extended to be an action on all subsets of Ω. We say that S is `-homogeneous provided it can send A to B for any two (not necessarily distinct) `-subsets A and B of Ω. On the condition that k ≤ ` < k + ` ≤ |Ω|, we show that every `-homogeneous transformation semigroup acting on Ω must be k-homogeneous. We report other variants of this result for Boolean lattices and projective geometries. In general, any semigroup action on a poset gives rise to an automaton and we associate some sequences of integers with the phase space of this automaton. When the poset is a geometric lattice, we propose to study various possible regularity properties of these sequences, especially the so-called top-heavy property.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"465 1","pages":"4"},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77471286","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}
Pub Date : 2022-02-09DOI: 10.26493/1855-3974.1970.29e
Jurij Kovič, T. Pisanski, Sara Sabrina Zemljič, A. Žitnik
{"title":"The Sierpiński product of graphs","authors":"Jurij Kovič, T. Pisanski, Sara Sabrina Zemljič, A. Žitnik","doi":"10.26493/1855-3974.1970.29e","DOIUrl":"https://doi.org/10.26493/1855-3974.1970.29e","url":null,"abstract":"","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75466950","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}
Pub Date : 2022-01-12DOI: 10.26493/1855-3974.2714.9b3
M. Brunetti, Z. Stanić
{"title":"Ordering signed graphs with large index","authors":"M. Brunetti, Z. Stanić","doi":"10.26493/1855-3974.2714.9b3","DOIUrl":"https://doi.org/10.26493/1855-3974.2714.9b3","url":null,"abstract":"","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"75 1","pages":"4"},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88442577","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}
Pub Date : 2022-01-01DOI: 10.26493/1855-3974.2691.0b7
M. Dodig, M. Stosic
In this paper we show that the generalized majorization of partitions of integers has a surprising completing-squares property. Together with the previously obtained transitivity-like property, this enables a compelling diagrammatical interpretation. Apart from purely combinatorial interest, the main result has applications in matrix completion problems, and representation theory of quivers.
{"title":"Double generalized majorization and diagrammatics","authors":"M. Dodig, M. Stosic","doi":"10.26493/1855-3974.2691.0b7","DOIUrl":"https://doi.org/10.26493/1855-3974.2691.0b7","url":null,"abstract":"In this paper we show that the generalized majorization of partitions of integers has a surprising completing-squares property. Together with the previously obtained transitivity-like property, this enables a compelling diagrammatical interpretation. Apart from purely combinatorial interest, the main result has applications in matrix completion problems, and representation theory of quivers.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81674472","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}
Pub Date : 2021-11-16DOI: 10.26493/1855-3974.2341.af2
M. Grannell, T. Griggs, G. Faro, A. Tripodi
There are ten configurations of two bowties that can arise in a bowtie system. The avoidance spectrum for three of these was determined in a previous paper (Aequat. Math. 85 (2013), 347–358). In this paper the avoidance spectrum for a further five configurations is determined.
{"title":"Avoidance in bowtie systems","authors":"M. Grannell, T. Griggs, G. Faro, A. Tripodi","doi":"10.26493/1855-3974.2341.af2","DOIUrl":"https://doi.org/10.26493/1855-3974.2341.af2","url":null,"abstract":"There are ten configurations of two bowties that can arise in a bowtie system. The avoidance spectrum for three of these was determined in a previous paper (Aequat. Math. 85 (2013), 347–358). In this paper the avoidance spectrum for a further five configurations is determined.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"15 1","pages":"3"},"PeriodicalIF":0.0,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87265589","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}
Pub Date : 2021-11-10DOI: 10.26493/1855-3974.2646.c07
Gašper Jaklič
{"title":"Cell reducing and the dimension of the C1 bivariate spline space","authors":"Gašper Jaklič","doi":"10.26493/1855-3974.2646.c07","DOIUrl":"https://doi.org/10.26493/1855-3974.2646.c07","url":null,"abstract":"","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"75 1","pages":"3"},"PeriodicalIF":0.0,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80582598","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}
Pub Date : 2021-11-09DOI: 10.26493/1855-3974.2645.8fc
M. Nazim, N. Rehman
{"title":"On the essential annihilating-ideal graph of commutative rings","authors":"M. Nazim, N. Rehman","doi":"10.26493/1855-3974.2645.8fc","DOIUrl":"https://doi.org/10.26493/1855-3974.2645.8fc","url":null,"abstract":"","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"27 1","pages":"3"},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87400524","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}
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