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 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. © 2012 Elsevier Ltd.
Merino, C., Noble, S. D., Ramírez-Ibáñez, M., & Villarroel-Flores, R. (2012). On the structure of the h-vector of a paving matroid. European Journal of Combinatorics, 33(8), 1787–1799. https://doi.org/10.1016/j.ejc.2012.04.002