On the Shape of a Pure $O$-Sequence

Mats Boij, Juan C. Migliore, Rosa M Miro-Roig, Uwe Nagel, Fabrizio Zanello (Autoren)

Buch | Softcover

78 Seiten

2012
American Mathematical Society (Verlag)
9780821869109 (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-13	9780821869109 / 9780821869109
Zustand	Neuware