Generic and special constructions of pure O-sequences
arXiv:1212.3426 · doi:10.1112/blms/bdu047
Abstract
It is shown that the h-vectors of Stanley-Reisner rings of three classes of matroids are pure O-sequences. The classes are (a) matroids that are truncations of other matroids, or more generally of Cohen-Macaulay complexes, (b) matroids whose dual is (rank + 2)-partite, and (c) matroids of Cohen-Macaulay type at most five. Consequences for the computational search for a counterexample to a conjecture of Stanley are discussed.
16 pages, v2: various small improvements, accepted by Bulletin of the London Math. Society