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

IF 0.3 4区数学 Q4 MATHEMATICS

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

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

引用次数: 0

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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混合小度中$f$-理想和$f$–理想的密度

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.