English

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

R2 v1 2026-07-22T17:14:30.830Z