Abstract
Let C be a clutter and let A be its incidence matrix. If the linear system x ≥ 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.
Original language | English |
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Pages (from-to) | 801-811 |
Number of pages | 11 |
Journal | Anais da Academia Brasileira de Ciencias |
Volume | 82 |
Issue number | 4 |
DOIs | |
State | Published - 2010 |
Keywords
- A-invariant
- Canonical module
- Ehrhart ring
- Integer rounding property
- Maximal cliques
- Normal ideal
- Perfect graph
- Rees algebra