Symmetric iterated Betti numbers

Details Symmetric iterated Betti numbers Symmetric iterated Betti numbers

2002-06-07

arxiv.org/abs/math/0206063v1

Mathematics

Combinatorics

20 pages, 2 figures

Scientific paper

We define a set of invariants of a homogeneous ideal $I$ in a polynomial ring called the symmetric iterated Betti numbers of $I$. For $I_{\Gamma}$, the Stanley-Reisner ideal of a simplicial complex $\Gamma$, these numbers are the symmetric counterparts of the exterior iterated Betti numbers of $\Gamma$ introduced by Duval and Rose. We show that the symmetric iterated Betti numbers of an ideal $I$ coincide with those of a particular reverse lexicographic generic initial ideal $\Gin(I)$ of $I$, and interpret these invariants in terms of the associated primes and standard pairs of $\Gin(I)$. We verify that for an ideal $I=I_\Gamma$ the extremal Betti numbers of $I_\Gamma$ are precisely the extremal (symmetric or exterior) iterated Betti numbers of $\Gamma$. We close with some results and conjectures about the relationship between symmetric and exterior iterated Betti numbers of a simplicial complex.

Affiliated with

Also associated with

No associations

Rating

Symmetric iterated Betti numbers 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 Symmetric iterated Betti numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetric iterated Betti numbers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-522517