Borel generators
Commutative Algebra
2010-11-03 v2 Combinatorics
Abstract
We use the notion of Borel generators to give alternative methods for computing standard invariants, such as associated primes, Hilbert series, and Betti numbers, of Borel ideals. Because there are generally few Borel generators relative to ordinary generators, this enables one to do manual computations much more easily. Moreover, this perspective allows us to find new connections to combinatorics involving Catalan numbers and their generalizations. We conclude with a surprising result relating the Betti numbers of certain principal Borel ideals to the number of pointed pseudo-triangulations of particular planar point sets.
Cite
@article{arxiv.1006.1436,
title = {Borel generators},
author = {Christopher A. Francisco and Jeffrey Mermin and Jay Schweig},
journal= {arXiv preprint arXiv:1006.1436},
year = {2010}
}
Comments
23 pages, 2 figures; very minor changes in v2. To appear in J. Algebra