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

@article{Merino2012OnTS,
  title={On the structure of the h-vector of a paving matroid},
  author={Criel Merino and Steven D. Noble and Marcelino Ram{\'i}rez-Ib{\'a}{\~n}ez and R. Villarroel-Flores},
  journal={Eur. J. Comb.},
  year={2012},
  volume={33},
  pages={1787-1799}
}
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. 

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