The Betti numbers of forests

Details The Betti numbers of forests The Betti numbers of forests

2005-01-14

arxiv.org/abs/math/0501226v2

Mathematics

Commutative Algebra

12 pages

Scientific paper

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.

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