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arXiv · 1804.00686

Newton complementary duals of $f$-ideals

Samuel Budd·Adam Van Tuyl
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Abstract

A square-free monomial ideal $I$ of $k[x_1,\ldots,x_n]$ is said to be an $f$-ideal if the facet complex and non-face complex associated with $I$ have the same $f$-vector. We show that $I$ is an $f$-ideal if and only if its Newton complementary dual $\widehat{I}$ is also an $f$-ideal. Because of this duality, previous results about some classes of $f$-ideals can be extended to a much larger class of $f$-ideals. An interesting by-product of our work is an alternative formulation of the Kruskal-Katona theorem for $f$-vectors of simplicial complexes.

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Samuel Budd, Adam Van Tuyl. 2018-04-02. Newton complementary duals of $f$-ideals. https://doi.org/10.4153/s0008439518000024

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