混合小度中$f$-理想和$f$–理想的密度

Pub Date : 2020-11-05 DOI:10.7146/math.scand.a-129244

HÀ Huytài, Graham Keiper, H. Mahmood, Jonathan L. O'Rourke

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摘要

如果一个方折射单项式理想的Stanley–Reisner和facet单纯复形具有相同的$f$-向量，则称之为$f$-理想。我们证明了当变量的数量达到无穷大时，在固定度上生成的$f$-理想具有渐近密度零。我们还提供了新的算法来构造小度生成的$f$-理想。

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

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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