ON THE (n, d)th f-IDEALS
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For a field K, a square-free monomial ideal I of K[x1, . . . , xn] 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 ≥ 2 and n ≥ d + 2, and we also give some algorithms to construct (n, d)th f-ideals.
Abstract
For a field K, a square-free monomial ideal I of K[x1, . . . , xn] 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 ≥ 2 and n ≥ d + 2, and we also give some algorithms to construct (n, d)th f-ideals.
참고문헌 (12)
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