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.
- Pub Date:
- December 2012
- Mathematics - Commutative Algebra;
- Mathematics - Combinatorics;
- 05E40 (Primary) 13D40;
- 13F55 (Secondary)
- 16 pages, v2: various small improvements, accepted by Bulletin of the London Math. Society