The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of containment.
In the shadows of a hypergraph: looking for associated primes of powers of square-free monomial ideals / Bela, E.; Favacchio, G.; Tran, N.. - In: JOURNAL OF ALGEBRAIC COMBINATORICS. - ISSN 0925-9899. - STAMPA. - (In corso di stampa).
Titolo: | In the shadows of a hypergraph: looking for associated primes of powers of square-free monomial ideals |
Autori: | |
Data di pubblicazione: | Being printed |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10801-019-00915-5 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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postprint draft - InTheShadowsOfAHypergraph.pdf | Articolo principale | 2. Post-print / Author's Accepted Manuscript | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
preprint revised - BelaFavacchioTran.pdf | Articolo principale | 1. Preprint / Submitted Version | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
Bela2019_Article_InTheShadowsOfAHypergraphLooki (1).pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2859712