Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2013.12.05
  • Published : 2015.06.01
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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.

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Acknowledgement

Supported by : National Natural Science Foundation of China

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  1. On the connectedness of f-simplicial complexes vol.16, pp.01, 2017, https://doi.org/10.1142/S0219498817500177
  2. F-ideals and f-graphs vol.45, pp.8, 2017, https://doi.org/10.1080/00927872.2016.1236119