HILBERT-FUNCTIONS OF COHEN-MACAULAY INTEGRAL-DOMAINS AND CHAIN-CONDITIONS OF FINITE PARTIALLY ORDERED SETS

[摘要] Let A = A0 + A1 + ... be a commutative graded ring such that (i) A0 = k a field, (ii) A = k[A1] and (iii) dim(k) A1 < infinity. It is a fundamental fact that the formal power series SIGMA-n = 0 infinity (dim(k) A(n))lambda-n is of the form (h0 + h1-lambda + ... + h(s)lambda-s)/(1 - lambda)dimA, where each h(i) is an integer. We are interested in the sequence (h0, h1, ..., h(s)), called the 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, see Corollary 2.11.

[发布日期] 1991-07-26