Pure $\mathcal{O}$-sequences arising from $2$-dimensional PS ear-decomposable simplicial complexes
Combinatorics
2018-11-12 v1
Abstract
We show that the -vector of a -dimensional PS ear-decomposable simplicial complex is a pure -sequence. This provides a strengthening of Stanley's conjecture for matroid -vectors in rank . Our approach modifies the approach of combinatorial shifting for arbitrary simplicial complexes to the setting of -dimensional PS ear-decomposable complexes, which allows us to greedily construct a corresponding pure multicomplex.
Cite
@article{arxiv.1811.04059,
title = {Pure $\mathcal{O}$-sequences arising from $2$-dimensional PS ear-decomposable simplicial complexes},
author = {Steven Klee and Brian Nugent},
journal= {arXiv preprint arXiv:1811.04059},
year = {2018}
}