On the Shape of a Pure $O$-Sequence
Seiten
2012
American Mathematical Society (Verlag)
978-0-8218-6910-9 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-6910-9 (ISBN)
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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.
Reihe/Serie | Memoirs of the American Mathematical Society |
---|---|
Verlagsort | Providence |
Sprache | englisch |
Gewicht | 300 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-8218-6910-8 / 0821869108 |
ISBN-13 | 978-0-8218-6910-9 / 9780821869109 |
Zustand | Neuware |
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