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Betti splittings and multigraded Betti numbers of cover ideals of bipartite graphs
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In this paper, we study Betti splittings of cover ideals of bipartite graphs. We prove that if [Formula: see text] is the cover ideal of a bipartite graph then the [Formula: see text]-partition of [Formula: see text] is a Betti splitting for any [Formula: see text]. We also prove that multigraded Betti numbers of any squarefree monomial ideal can appear in a certain part of multigraded Betti numbers of the cover ideal of a bipartite graph.
World Scientific Pub Co Pte Ltd
Title: Betti splittings and multigraded Betti numbers of cover ideals of bipartite graphs
Description:
In this paper, we study Betti splittings of cover ideals of bipartite graphs.
We prove that if [Formula: see text] is the cover ideal of a bipartite graph then the [Formula: see text]-partition of [Formula: see text] is a Betti splitting for any [Formula: see text].
We also prove that multigraded Betti numbers of any squarefree monomial ideal can appear in a certain part of multigraded Betti numbers of the cover ideal of a bipartite graph.
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