ON THE (n, d)th f-IDEALS

Title & Authors
ON THE (n, d)th f-IDEALS
GUO, JIN; WU, TONGSUO;

Abstract
For a field K, a square-free monomial ideal I of K[$\small{x_1}$, . . ., $\small{x_n}$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $\small{(n, d)^{th}}$ f-ideal. In this paper, we prove the existence of $\small{(n, d)^{th}}$ f-ideal for $\small{d{\geq}2}$ and $\small{n{\geq}d+2}$, and we also give some algorithms to construct $\small{(n, d)^{th}}$ f-ideals.
Keywords
perfect set;f-ideal;unmixed f-ideal;perfect number;
Language
English
Cited by
1.
On the connectedness of f-simplicial complexes, Journal of Algebra and Its Applications, 2017, 16, 01, 1750017
2.
F-ideals and f-graphs, Communications in Algebra, 2017, 45, 8, 3207
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