(k\)-clean monomial ideals

In this paper, we introduce the concept of \(k\)-clean monomial ideals as an extension of clean monomial ideals and present some homological and combinatorial properties of them. Using the hierarchal structure of \(k\)-clean ideals, we show that a \((d-1)\)-dimensional simplicial complex is \(k\)-de...

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Bibliographic Details
Published inarXiv.org
Main Author Rahmati-Asghar, Rahim
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 24.02.2017
Subjects
Combinatorial analysis
Homology
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Summary:In this paper, we introduce the concept of \(k\)-clean monomial ideals as an extension of clean monomial ideals and present some homological and combinatorial properties of them. Using the hierarchal structure of \(k\)-clean ideals, we show that a \((d-1)\)-dimensional simplicial complex is \(k\)-decomposable if and only if its Stanley-Reisner ideal is \(k\)-clean, where \(k\leq d-1\). We prove that the classes of monomial ideals like monomial complete intersection ideals, Cohen-Macaulay monomial ideals of codimension 2 and symbolic powers of Stanley-Reisner ideals of matroid complexes are \(k\)-clean for all \(k\geq 0\).
ISSN:2331-8422