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- W2042207841 abstract "Let A = A 0 ⊕ A 1 ⊕ ⋯ be a commutative graded ring such that (i) A 0 = k a field. (ii) A = k [ A 1 ] and (iii) dim k A 1 < ∞. It is a fundamental fact that the formal power series ∑ ∗ n=0 (dim λ A n )λ n is of the form ( h 0 + h 1 λ + ⋯ + h 8 λ x )/(1-λ) dim A , where each h , is an integer. We are interested in the sequence ( h 0 , h 1 ,…, h x ) called tL. h -vector of A , when A is a Cohen-Macaulay integral domain. In this paper, first, in Section 1, we summarize the basic information on the h -vector of A which can be obtained by investigating the behavior of the canonical module K A of A . Secondly, in Section 2, we apply the abstract theory in Section 1 to the combinatorial problem of finding a characterization of the so-called w -vectors of finite partially ordered sets and obtain linear and nonlinear inequalities for the w -vector of a finite partially ordered set which satisfies a certain chain condition." @default.
- W2042207841 created "2016-06-24" @default.
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- W2042207841 date "1991-07-01" @default.
- W2042207841 modified "2023-09-28" @default.
- W2042207841 title "Hilbert functions of Cohen— Macaulay integral domains and chain conditions of finite partially ordered sets" @default.
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- W2042207841 doi "https://doi.org/10.1016/0022-4049(91)90065-a" @default.
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