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Item Details
| Title:
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ON THE SHAPE OF A PURE O-SEQUENCE
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| By: |
Mats Boij, Juan C. Migliore, Rosa Maria Miro-Roig |
| Format: |
Paperback |
| List price:
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£56.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821869108 |
| ISBN 13: |
9780821869109 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 June, 2012 |
| Series: |
Memoirs of the American Mathematical Society 218, 1024 |
| Pages: |
78 |
| Description: |
"July 2012, volume 218, number 1024 (second of 5 numbers)." |
| Synopsis: |
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. |
| Illustrations: |
Illustrations |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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