Distributive Lattices, Bipartite Graphs and Alexander Duality

Details Distributive Lattices, Bipartite Graphs and Alexander Duality Distributive Lattices, Bipartite Graphs and Alexander Duality

2003-07-17

arxiv.org/abs/math/0307235v1

Mathematics

Commutative Algebra

Scientific paper

A certain squarefree monomial ideal $H_P$ arising from a finite partially ordered set $P$ will be studied from viewpoints of both commutative algebra and combinatorics. First, it is proved that the defining ideal of the Rees algebra of $H_P$ possesses a quadratic Gr\"obner basis. Thus in particular all powers of $H_P$ have linear resolutions. Second, the minimal free graded resolution of $H_P$ will be constructed explicitly and a combinatorial formula to compute the Betti numbers of $H_P$ will be presented. Third, by using the fact that the Alexander dual of the simplicial complex $\Delta$ whose Stanley--Reisner ideal coincides with $H_P$ is Cohen--Macaulay, all the Cohen--Macaulay bipartite graphs will be classified.

Affiliated with

Also associated with

No associations

Rating

Distributive Lattices, Bipartite Graphs and Alexander Duality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Distributive Lattices, Bipartite Graphs and Alexander Duality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Distributive Lattices, Bipartite Graphs and Alexander Duality will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-152097