The Betti numbers of forests
Commutative Algebra
2007-05-23 v2 Combinatorics
Abstract
This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs.
Keywords
Cite
@article{arxiv.math/0501226,
title = {The Betti numbers of forests},
author = {Sean Jacques and Mordechai Katzman},
journal= {arXiv preprint arXiv:math/0501226},
year = {2007}
}
Comments
12 pages