The Hopf monoid of Megagreedoids
Combinatorics
2018-02-14 v1
Abstract
We introduce megagreedoids, which generalize polymatroids, megamatroids, and greedoids. We define a quasisymmetric function invariant for a megagreedoid, and show that it has a positive expansion in the basis of fundamental quasisymmetric functions. Our proof involves lexicographic shellability. We also show that megagreedoids form a Hopf monoid. A running example is a megagreedoid associated to a rooted connected graph, and the resulting generalization of the chromatic symmetric function.
Keywords
Cite
@article{arxiv.1802.04386,
title = {The Hopf monoid of Megagreedoids},
author = {Jacob A White},
journal= {arXiv preprint arXiv:1802.04386},
year = {2018}
}
Comments
11 pages, 4 figures, submitted to FPSAC. Comments welcome (and any recommendations about alternative names to 'megagreedoid' are particularly encouraged)