{"title":"Shellable flag simplicial complexes of non-simple polyominoes","authors":"Francesco Navarra","doi":"arxiv-2408.12367","DOIUrl":"https://doi.org/arxiv-2408.12367","url":null,"abstract":"In this article we investigate the shellability of the flag simplicial\u0000complexes attached to non-simple and thin polyominoes. As a consequence, we\u0000obtain the Cohen-Macaulayness and a combinatorial interepetation of the\u0000$h$-polynomial of the related coordinate rings.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185606","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}
{"title":"$φ$-$δ$-$S$-primary hyperideals","authors":"Mahdi Anbarloei","doi":"arxiv-2408.12241","DOIUrl":"https://doi.org/arxiv-2408.12241","url":null,"abstract":"Among many generalizations of primary hyperideals, weakly $n$-ary primary\u0000hyperideals and $n$-ary $S$-primary hyperideals have been studied recently. Let\u0000$S$ be an $n$-ary multiplicative set of a commutative Krasner $(m,n)$-hyperring\u0000$K$ and, $phi$ and $delta$ be reduction and expansion functions of\u0000hyperideals of $K$, respectively. The purpose of this paper is to introduce\u0000$n$-ary $phi$-$delta$-$S$-primary hyperideals which serve as an extension of\u0000$S$-primary hyperideals with the help of $phi$ and $delta$. We present some\u0000main results and examples explaining the sructure of this concept. We examine\u0000the relations of $n$-ary $S$-primary hyperideals with other classes of\u0000hyperideals and give some ways to connect them. Moreover, we give some\u0000characterizations of this notion on direct product of commutative Krasner $(m,\u0000n)$-hyperrings.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185609","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}
{"title":"On the deletion and addition of a conic to a free curve","authors":"Anca Macinic","doi":"arxiv-2408.11714","DOIUrl":"https://doi.org/arxiv-2408.11714","url":null,"abstract":"We describe the behaviour of a free conic-line arrangement to the deletion,\u0000respectively addition, of a smooth conic. Along the way we derive some\u0000restrictions on the geometry of a conic-line arrangement induced by the\u0000freeness property. We show the same behaviour extends to free reduced curves in\u0000general.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185610","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}
{"title":"Supertropical Monoids III: Factorization and splitting covers","authors":"Zur Izhakian, Manfred Knebusch","doi":"arxiv-2408.10772","DOIUrl":"https://doi.org/arxiv-2408.10772","url":null,"abstract":"The category $STROP_m$ of supertropical monoids, whose morphisms are\u0000transmissions, has the full--reflective subcategory $STROP$ of commutative\u0000semirings. In this setup, quotients are determined directly by equivalence\u0000relations, as ideals are not applicable for monoids, leading to a new approach\u0000to factorization theory. To this end, tangible factorization into irreducibles\u0000is obtained through fiber contractions and their hierarchy. Fiber contractions\u0000also provide different quotient structures, associated with covers and types of\u0000splitting covers.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185611","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}
{"title":"A note on $S$-flat preenvelopes","authors":"Xiaolei Zhang","doi":"arxiv-2408.10523","DOIUrl":"https://doi.org/arxiv-2408.10523","url":null,"abstract":"In this note, we investigate the notion of $S$-flat preenvelopes of modules.\u0000In particular, we give an example that a ring $R$ being coherent does not imply\u0000that every $R$-module have an $S$-flat preenvelope, giving a negative answer to\u0000the question proposed by Bennis and Bouziri cite{BB24}. Besides, we also show\u0000that $R_S$ is a coherent ring also does not imply that $R$ is an $S$-coherent\u0000ring in general.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185612","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}
Mandala von Westenholz, Martin Atzmueller, Tim Römer
{"title":"Simplicial complexes in network intrusion profiling","authors":"Mandala von Westenholz, Martin Atzmueller, Tim Römer","doi":"arxiv-2408.09788","DOIUrl":"https://doi.org/arxiv-2408.09788","url":null,"abstract":"For studying intrusion detection data we consider data points referring to\u0000individual IP addresses and their connections: We build networks associated\u0000with those data points, such that vertices in a graph are associated via the\u0000respective IP addresses, with the key property that attacked data points are\u0000part of the structure of the network. More precisely, we propose a novel\u0000approach using simplicial complexes to model the desired network and the\u0000respective intrusions in terms of simplicial attributes thus generalizing\u0000previous graph-based approaches. Adapted network centrality measures related to\u0000simplicial complexes yield so-called patterns associated to vertices, which\u0000themselves contain a set of features. These are then used to describe the\u0000attacked or the attacker vertices, respectively. Comparing this new strategy\u0000with classical concepts demonstrates the advantages of the presented approach\u0000using simplicial features for detecting and characterizing intrusions.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185613","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}
{"title":"Generic orbit recovery from invariants of very low degree","authors":"Dan Edidin, Josh Katz","doi":"arxiv-2408.09599","DOIUrl":"https://doi.org/arxiv-2408.09599","url":null,"abstract":"Motivated by the multi-reference alignment (MRA) problem and questions in\u0000equivariant neural networks we study the problem of recovering the generic\u0000orbit in a representation of a finite group from invariant tensors of degree at\u0000most three. We explore the similarities and differences between the descriptive\u0000power of low degree polynomial and unitary invariant tensors and provide\u0000evidence that in many cases of interest they have similar descriptive power. In\u0000particular we prove that for the regular representation of a finite group,\u0000polynomial invariants of degree at most three separate generic orbits answering\u0000a question posed in cite{bandeira2017estimation}. This complements a\u0000previously known result for unitary invariants~cite{smach2008generalized}. We\u0000also investigate these questions for subregular representations of finite\u0000groups and prove that for the defining representation of the dihedral group,\u0000polynomial invariants of degree at most three separate generic orbits. This\u0000answers a question posed in~cite{bendory2022dihedral} and it implies that the\u0000sample complexity of the corresponding MRA problem is $sim sigma^6$. On the\u0000other hand we also show that for the groups $D_n$ and $A_4$ generic orbits in\u0000the {em complete multiplicity-free} representation cannot be separated by\u0000invariants of degree at most three.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185614","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}
{"title":"The splitting of the de Rham cohomology of soft function algebras is multiplicative","authors":"Igor Baskov","doi":"arxiv-2408.08689","DOIUrl":"https://doi.org/arxiv-2408.08689","url":null,"abstract":"Let $A$ be a real soft function algebra. In arXiv:2208.11431 we have obtained\u0000a canonical splitting $mathrm{H}^* (Omega ^bullet _{A|mathrm{R}}) cong\u0000mathrm{H} ^* (X,mathrm{R})oplus text{(something)}$ via the canonical maps\u0000$Lambda_A:mathrm{H} ^* (X,mathrm{R})tomathrm{H} ^* (Omega ^bullet\u0000_{A|mathrm{R}})$ and $Psi_A:mathrm{H} ^* (Omega ^bullet\u0000_{A|mathrm{R}})tomathrm{H} ^* (X,mathrm{R})$. In this paper we prove that\u0000these maps are multiplicative.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185616","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}
{"title":"A special subring of the Nagata ring and the Serre's conjecture ring","authors":"Hyungtae Baek, Jung Wook Lim","doi":"arxiv-2408.08758","DOIUrl":"https://doi.org/arxiv-2408.08758","url":null,"abstract":"Many ring theorists researched various properties of Nagata rings and Serre's\u0000conjecture rings. In this paper, we introduce a subring (refer to the Anderson\u0000ring) of both the Nagata ring and the Serre's conjecture ring (up to\u0000isomorphism), and investigate properties of the Anderson rings. Additionally,\u0000we compare the properties of the Anderson rings with those of Nagata rings and\u0000Serre's conjecture rings.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185615","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}
{"title":"First Coefficient ideals and $R_1$ property of Rees algebras","authors":"Tony J. Puthenpurakal","doi":"arxiv-2408.05532","DOIUrl":"https://doi.org/arxiv-2408.05532","url":null,"abstract":"Let $(A,mathfrak{m})$ be an excellent normal local ring of dimension $d geq\u00002$ with infinite residue field. Let $I$ be an $mathfrak{m}$-primary ideal.\u0000Then the following assertions are equivalent: (i) The extended Rees algebra $A[It, t^{-1}]$ is $R_1$. (ii) The Rees algebra $A[It]$ is $R_1$. (iii) $Proj(A[It])$ is $R_1$. (iv) $(I^n)^* = (I^n)_1$ for all $n geq 1$. Here $(I^n)^*$ is the integral closure of $I^n$ and $(I^n)_1$ is the first\u0000coefficient ideal of $I^n$.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185618","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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