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arXiv · 2011.03067

Density of $f$-ideals and $f$-ideals in mixed small degrees

Huy TÀi HÀ·Graham Keiper·Hasan Mahmood·Jonathan L. O'Rourke
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Abstract

A squarefree monomial ideal is called an $f$-ideal if its Stanley-Reisner and facet simplicial complexes have the same $f$-vector. We show that $f$-ideals generated in a fixed degree have asymptotic density zero when the number of variables goes to infinity. We also provide novel algorithms to construct $f$-ideals generated in small degrees.

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Huy TÀi HÀ, Graham Keiper, Hasan Mahmood, Jonathan L. O'Rourke. 2020-11-05. Density of $f$-ideals and $f$-ideals in mixed small degrees. https://arxiv.org/abs/2011.03067

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