Geodesic
Squarefree monomial ideals with maximal depth
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1111-1124
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Let $(R,\mathfrak m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. We say $M$ has maximal depth if there is an associated prime $\mathfrak p$ of $M$ such that depth $M=\dim R/\mathfrak p$. In this paper we study squarefree monomial ideals which have maximal depth. Edge ideals of cycle graphs, transversal polymatroidal ideals and high powers of connected bipartite graphs with this property are classified.
Let $(R,\mathfrak m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. We say $M$ has maximal depth if there is an associated prime $\mathfrak p$ of $M$ such that depth $M=\dim R/\mathfrak p$. In this paper we study squarefree monomial ideals which have maximal depth. Edge ideals of cycle graphs, transversal polymatroidal ideals and high powers of connected bipartite graphs with this property are classified.
DOI : 10.21136/CMJ.2020.0171-19
Classification : 05E40, 13C15
Keywords: maximal depth; cycle graph; line graph; whisker graph; transversal polymatroidal ideal; power of edge ideal 
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Rahimi, Ahad. Squarefree monomial ideals with maximal depth. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1111-1124. doi: 10.21136/CMJ.2020.0171-19

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