On the shape of a pure Osequence
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, 2012.
 Physical description
 vii, 78 p. : ill ; 26 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1024.
Access
Available online

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QA3 .A57 NO.1024

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QA3 .A57 NO.1024
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Contributors
 Contributor
 Boij, Mats, 1969
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Introduction
 Definitions and preliminary results
 Differentiability and unimodality
 The interval conjecture for pure Osequences
 Enumerating pure Osequences
 Monomial artinian level algebras of type two in three variables
 Failure of the WLP and SLP
 Remarks on pure fvectors
 Some open or openended problems.
 Publisher's Summary
 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Mats Boij ... [et al.].
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1024
 Note
 "July 2012, volume 218, number 1024 (second of 5 numbers)."
 ISBN
 9780821869109
 0821869108