Flawless 0-sequences and Hilbert functions of Cohen-Macaulay integral domains |
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Authors: | Takayuki Hibi |
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Institution: | Department of Mathematics, Faculty of Science, Nagoya University, Chikasa-ku, Nagoya 464, Japan |
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Abstract: | Let A = A0A1 be a commutative graded ring such that (i) A0 = k a field, (ii) A = kA1] and (iii) dimk A1 < ∞. It is well known that the formal power series ∑∞n = 0 (dimkAn)λ n is of the form (h0 + h1λ + + hsλs)/(1 ? λ)dimA with each hiε
. We are interested in the sequence (h0, h1,…,hs), called the h-vector of A, when A is a Cohen–Macaulay integral domain. In this paper, after summarizing fundamental results (Section 1), we study h-vectors of certain Gorenstein domains (Section 2) and find some examples of h-vectors arising from integrally closed level domains (Sections 3 and 4). |
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