Pure O-Sequences arising from 2-Dimensional PS Ear-Decomposable Simplicial Complexes - Klee, Steven; Nugent, Brian (The Electronic Journal of Combinatorics, 2020)
We show that the h-vector of a 2-dimensional PS ear-decomposable simplicial complex is a pure O-sequence. This provides a strengthening of Stanley’s conjecture for matroid h-vectors in rank 3. Our approach modifies the approach of combinatorial shifting for arbitrary simplicial complexes to the setting of 2-dimensional PS ear-decomposable complexes, which allows us to greedily construct pure multicomplex corresponding to each PS ear-decomposable complex.