On the Shape of a Pure $O$-Sequence

On the Shape of a Pure $O$-Sequence
Author :
Publisher : American Mathematical Soc.
Total Pages : 93
Release :
ISBN-10 : 9780821869109
ISBN-13 : 0821869108
Rating : 4/5 (108 Downloads)

Book Synopsis On the Shape of a Pure $O$-Sequence by : Mats Boij

Download or read book On the Shape of a Pure $O$-Sequence written by Mats Boij and published by American Mathematical Soc.. This book was released on 2012 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monomial order ideal is a finite collection X of (monic) monomials such that, whenever M∈X and N divides M, then N∈X. Hence X is a poset, where the partial order is given by divisibility. If all, say t t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h_=(h0=1,h1,...,he), 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 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 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.


On the Shape of a Pure $O$-Sequence Related Books

On the Shape of a Pure $O$-Sequence
Language: en
Pages: 93
Authors: Mats Boij
Categories: Mathematics
Type: BOOK - Published: 2012 - Publisher: American Mathematical Soc.

GET EBOOK

A monomial order ideal is a finite collection X of (monic) monomials such that, whenever M∈X and N divides M, then N∈X. Hence X is a poset, where the partia
Infinite-Dimensional Representations of 2-Groups
Language: en
Pages: 133
Authors: John C. Baez
Categories: Mathematics
Type: BOOK - Published: 2012 - Publisher: American Mathematical Soc.

GET EBOOK

Just as groups can have representations on vector spaces, 2-groups have representations on 2-vector spaces, but Lie 2-groups typically have few representations
Extended Graphical Calculus for Categorified Quantum sl(2)
Language: en
Pages: 100
Authors: Mikhail Khovanov
Categories: Mathematics
Type: BOOK - Published: 2012 - Publisher: American Mathematical Soc.

GET EBOOK

In an earlier paper, Aaron D. Lauda constructed a categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2); here he, Khovanov, Marco Macka
Elliptic Partial Differential Equations with Almost-Real Coefficients
Language: en
Pages: 120
Authors: Ariel Barton
Categories: Mathematics
Type: BOOK - Published: 2013-04-22 - Publisher: American Mathematical Soc.

GET EBOOK

In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrice
The Reductive Subgroups of $F_4$
Language: en
Pages: 100
Authors: David I. Stewart
Categories: Mathematics
Type: BOOK - Published: 2013-04-22 - Publisher: American Mathematical Soc.

GET EBOOK

Let $G=G(K)$ be a simple algebraic group defined over an algebraically closed field $K$ of characteristic $p\geq 0$. A subgroup $X$ of $G$ is said to be $G$-com