{"title":"Stanley-Reisner Ideals with Pure Resolutions","authors":"David Carey, Moty Katzman","doi":"arxiv-2409.05481","DOIUrl":null,"url":null,"abstract":"We investigate Stanley-Reisner ideals with pure resolutions. To do this, we\nintroduce the family of PR complexes, simplicial complexes whose dual\nStanley-Reisner ideals have pure resolutions. We present two infinite families\nof highly-symmetric PR complexes. We also prove a partial analogue to the first\nBoij-S\\\"{o}derberg Conjecture for Stanley-Reisner ideals, by detailing an\nalgorithm for constructing Stanley-Reisner ideals with pure Betti diagrams of\nany given shape, save for the initial shift $c_0$.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05481","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate Stanley-Reisner ideals with pure resolutions. To do this, we
introduce the family of PR complexes, simplicial complexes whose dual
Stanley-Reisner ideals have pure resolutions. We present two infinite families
of highly-symmetric PR complexes. We also prove a partial analogue to the first
Boij-S\"{o}derberg Conjecture for Stanley-Reisner ideals, by detailing an
algorithm for constructing Stanley-Reisner ideals with pure Betti diagrams of
any given shape, save for the initial shift $c_0$.
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