Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution |
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Authors: | E Connon S Faridi |
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Institution: | Department of Mathematics and Statistics, Dalhousie University, Canada |
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Abstract: | In this paper we extend one direction of Fröberg?s theorem on a combinatorial classification of quadratic monomial ideals with linear resolutions. We do this by generalizing the notion of a chordal graph to higher dimensions with the introduction of d-chorded and orientably-d-cycle-complete simplicial complexes. We show that a certain class of simplicial complexes, the d-dimensional trees, correspond to ideals having linear resolutions over fields of characteristic 2 and we also give a necessary combinatorial condition for a monomial ideal to be componentwise linear over all fields. |
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Keywords: | Linear resolution Monomial ideal Chordal graph Simplicial complex Simplicial homology Stanley–Reisner complex Facet complex Chordal hypergraph |
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