Title

Pure O-Sequences and Matroid h-Vectors

Authors

Huy Tai Ha, Tulane University
Erik Stokes, Rose-Hulman Institute of Technology
Fabrizio Zanello, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

9-2013

Abstract

We study Stanley’s long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable artinian level monomial ideals, as often done in the past, to the study of properties of pure O-sequences. We propose a conjecture on pure O-sequences and settle it in small socle degrees. This allows us to prove Stanley’s conjecture for all matroids of rank 3. At the end of the paper, using our method, we discuss a first possible approach to Stanley’s conjecture in full generality. Our technical work on pure O-sequences also uses very recent results of the third author and collaborators.

Publisher's Statement

© Springer Basel 2013. Publisher’s version of record: https://doi.org/10.1007/s00026-013-0193-6

Publication Title

Annals of Combinatorics

Recommended Citation

Ha, H. T., Stokes, E., & Zanello, F. (2013). Pure O-Sequences and Matroid h-Vectors. Annals of Combinatorics, 17(3), 495-508. http://doi.org/10.1007/s00026-013-0193-6
Retrieved from: https://digitalcommons.mtu.edu/math-fp/51