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http://dx.doi.org/10.4134/JKMS.2015.52.4.685

ON THE (n, d)th f-IDEALS  

GUO, JIN (College of Information Science and Technology Hainan University)
WU, TONGSUO (Department of Mathematics Shanghai Jiaotong University)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.4, 2015 , pp. 685-697 More about this Journal
Abstract
For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] 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 $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.
Keywords
perfect set; f-ideal; unmixed f-ideal; perfect number;
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