On the shape of a pure O-sequence
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Bibliographic Information
On the shape of a pure O-sequence
（Memoirs of the American Mathematical Society, no. 1024）
American Mathematical Society, 2012, c2011
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Note
"July 2012, volume 218, number 1024 (second of 5 numbers)."
Includes bibliographical references (p. 75-78)
Description and Table of Contents
Description
A monomial order ideal is a finite collection $X$ of (monic) monomials such that, whenever $M\in X$ and $N$ divides $M$, then $N\in X$. Hence $X$ is a poset, where the partial order is given by divisibility. If all, say $t$, maximal monomials of $X$ have the same degree, then $X$ is pure (of type $t$). A pure $O$-sequence is the vector, $\underline{h}=(h_0=1,h_1,...,h_e)$, counting the monomials of $X$ in each degree. Equivalently, pure $O$-sequences can be characterized as the $f$-vectors of pure multicomplexes, or, in the language of commutative algebra, as the $h$-vectors of monomial Artinian level algebras. Pure $O$-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their $f$-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure $O$-sequences.
by "Nielsen BookData"
