✦ LIBER ✦

Matroid inequalities

✍ Scribed by Manoj K. Chari

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 188 KB
Volume: 147
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00122-d

No coin nor oath required. For personal study only.

✦ Synopsis

An important enumerative invariant of a matroid M of rank d is its h-vector defined as (ho, hi ..... ha), where h~ is the coefficient ofx d-i in the polynomial T(M; x, 1), where T(M; x, y) is the Tutte polynomial of M [3]. We refer to Bj6rner's chapter [1] and to [4] for a comprehensive discussion of the algebraic and topological aspects of this invariant and to [2] for a description of applications to network reliability. The combinatorial significance of the h-vector is due to its direct relation to the vector (fo, fl ..... fd), wheref~ is the number of independent sets of cardinality i. This relation is easily seen from the following one-variable specialization of Tutte's famous identity d d ~f/(x--1) a-' = ~ hixa-'= T(M;x, 1).

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