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arXiv · 1605.07727

Lattice Complements and the Subadditivity of Syzygies of Simplicial Forests

Sara Faridi
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Abstract

We prove the subadditivity property for the maximal degrees of the syzygies of facet ideals simplicial forests. For such an ideal $I$, if the $i$-th Betti number is nonzero and $i=a+b$, we show that there are monomials in the lcm lattice of $I$ that are complements in part of the lattice, each supporting a nonvanishing $a$-th and $b$-th Betti numbers. The subadditivity formula follows from this observation.

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Sara Faridi. 2016-05-25. Lattice Complements and the Subadditivity of Syzygies of Simplicial Forests. https://arxiv.org/abs/1605.07727

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