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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)
  • 투고 : 2013.12.05
  • 발행 : 2015.06.01

초록

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.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. G. Q. Abbasi, S. Ahmad, I. Anwar, and W. A. Baig, f-Ideals of degree 2, Algebra Colloq. 19 (2012), no. 1, 921-926. https://doi.org/10.1142/S1005386712000788
  2. I. Anwar, H. Mahmood, M. A. Binyamin, and M. K. Zafar, On the Characterization of f-Ideals, Comm. Algebra 42 (2014), no. 9, 3736-3741. https://doi.org/10.1080/00927872.2013.792092
  3. M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, MA, 1969.
  4. E. Connon and S. Faridi, Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution, J. Combinatorial Theory Ser. A 120 (2013), no. 7, 1714-1731. https://doi.org/10.1016/j.jcta.2013.05.009
  5. D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, 150. Springer-Verlag, New York, 1995.
  6. S. Faridi, The facet ideal of a simplicial complex, Manuscripta Math. 109 (2002), no. 2, 159-174. https://doi.org/10.1007/s00229-002-0293-9
  7. J. Guo, T. S. Wu, and Q. Liu, Perfect sets and f-Ideals, preprint.
  8. J. Herzog and T. Hibi, Monomial Ideals, Springer-Verlag London, Ltd., London, 2011.
  9. J. Herzog, T. Hibi, and X. Zheng, Dirac's theorem on chordal graphs and Alexander duality, European J. Combin. 25 (2004), no. 7, 949-960. https://doi.org/10.1016/j.ejc.2003.12.008
  10. R. H. Villarreal, Monomial Algebra, Marcel Dekker, Inc, New York, 2001.
  11. O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Reprints of the 1958-60 edition. Springer-Verlag New York, 1979.
  12. X. Zheng, Resolutions of facet ideals, Comm. Algebra 32 (2004), no. 6, 2301-2324. https://doi.org/10.1081/AGB-120037222

피인용 문헌

  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