On the structure of the h-vector of a paving matroid

Abstract

We give two proofs that the $h$-vector of any paving matroid is a pure O-sequence, thus answering in the affirmative a conjecture made by R. Stanley, for this particular class of matroids. We also investigate the problem of obtaining good lower bounds for the number of bases of a paving matroid given its rank and number of elements.

We've corrected typos and small mistakes in the previous version. We've also tidied up a few proofs and the references

References in corpus (2)

• The $h$-vectors of 1-dimensional Matroid Complexes and a Conjecture of Stanley
• Some inequalities for the Tutte polynomial

Cited by in corpus (2)

• Sparse paving matroids, basis-exchange properties, and cyclic flats
• Some inequalities for the Tutte polynomial