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Zeros of rank-generating functions of Cohen-Macaulay complexes

โœ Scribed by David G. Wagner

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
620 KB
Volume
139
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Many combinatorial polynomials are related to rank-generating functions of Cohen-Macaulay complexes; notable among these are reliability, chromatic, flow, Birkhoff, and order polynomials. We prove two analytic theorems on the location of zeros of polynomials which have direct applications to the rank-generating functions of Cohen-Macaulay complexes and discuss their consequences for each of the aforementioned classes of polynomials.

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Cohen-Macaulay Types of Cohen-Macaulay C
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โœ T. Hibi ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 750 KB

We say that a Cohen-Macaulay poset (partially ordered set) is "superior" if every open interxal \((x, y)\) of \(P^{*}\) with \(\mu_{p}(x, y) \neq 0\) is doubly Cohen-Macaulay. For example, if \(L=P^{\wedge}\) is a modular lattice, then the Cohen-Macaulay poset \(P\) is superior. We present a formula