Systems with the integer rounding property in normal monomial subrings

Detalhes bibliográficos
Autor(a) principal: Dupont,Luis A.
Data de Publicação: 2010
Outros Autores: Rentería-Márquez,Carlos, Villarreal,Rafael H.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652010000400002
Resumo: Let C be a clutter and let A be its incidence matrix. If the linear system x &gt; 0; x A < 1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a connected graph, we describe when the aforementioned linear system has the integer rounding property in combinatorial and algebraic terms using graph theory and the theory of Rees algebras. As a consequence we show that the extended Rees algebra of the edge ideal of a bipartite graph is Gorenstein if and only if the graph is unmixed.
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spelling Systems with the integer rounding property in normal monomial subringscanonical modulea-invariantnormal idealperfect graphmaximal cliquesRees algebraEhrhart ringinteger rounding propertyLet C be a clutter and let A be its incidence matrix. If the linear system x &gt; 0; x A < 1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a connected graph, we describe when the aforementioned linear system has the integer rounding property in combinatorial and algebraic terms using graph theory and the theory of Rees algebras. As a consequence we show that the extended Rees algebra of the edge ideal of a bipartite graph is Gorenstein if and only if the graph is unmixed.Academia Brasileira de Ciências2010-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652010000400002Anais da Academia Brasileira de Ciências v.82 n.4 2010reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652010000400002info:eu-repo/semantics/openAccessDupont,Luis A.Rentería-Márquez,CarlosVillarreal,Rafael H.eng2011-02-28T00:00:00Zoai:scielo:S0001-37652010000400002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2011-02-28T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Systems with the integer rounding property in normal monomial subrings
title Systems with the integer rounding property in normal monomial subrings
spellingShingle Systems with the integer rounding property in normal monomial subrings
Dupont,Luis A.
canonical module
a-invariant
normal ideal
perfect graph
maximal cliques
Rees algebra
Ehrhart ring
integer rounding property
title_short Systems with the integer rounding property in normal monomial subrings
title_full Systems with the integer rounding property in normal monomial subrings
title_fullStr Systems with the integer rounding property in normal monomial subrings
title_full_unstemmed Systems with the integer rounding property in normal monomial subrings
title_sort Systems with the integer rounding property in normal monomial subrings
author Dupont,Luis A.
author_facet Dupont,Luis A.
Rentería-Márquez,Carlos
Villarreal,Rafael H.
author_role author
author2 Rentería-Márquez,Carlos
Villarreal,Rafael H.
author2_role author
author
dc.contributor.author.fl_str_mv Dupont,Luis A.
Rentería-Márquez,Carlos
Villarreal,Rafael H.
dc.subject.por.fl_str_mv canonical module
a-invariant
normal ideal
perfect graph
maximal cliques
Rees algebra
Ehrhart ring
integer rounding property
topic canonical module
a-invariant
normal ideal
perfect graph
maximal cliques
Rees algebra
Ehrhart ring
integer rounding property
description Let C be a clutter and let A be its incidence matrix. If the linear system x &gt; 0; x A < 1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a connected graph, we describe when the aforementioned linear system has the integer rounding property in combinatorial and algebraic terms using graph theory and the theory of Rees algebras. As a consequence we show that the extended Rees algebra of the edge ideal of a bipartite graph is Gorenstein if and only if the graph is unmixed.
publishDate 2010
dc.date.none.fl_str_mv 2010-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652010000400002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652010000400002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652010000400002
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.82 n.4 2010
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
instacron_str ABC
institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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