Euler characteristic reciprocity for chromatic, flow and order polynomials
Combinatorics
2018-09-17 v2 Algebraic Geometry
Algebraic Topology
Abstract
The Euler characteristic of a semialgebraic set can be considered as a generalization of the cardinality of a finite set. An advantage of semialgebraic sets is that we can define "negative sets" to be the sets with negative Euler characteristics. Applying this idea to posets, we introduce the notion of semialgebraic posets. Using "negative posets", we establish Stanley's reciprocity theorems for order polynomials at the level of Euler characteristics. We also formulate the Euler characteristic reciprocities for chromatic and flow polynomials.
Cite
@article{arxiv.1601.00254,
title = {Euler characteristic reciprocity for chromatic, flow and order polynomials},
author = {Takahiro Hasebe and Toshinori Miyatani and Masahiko Yoshinaga},
journal= {arXiv preprint arXiv:1601.00254},
year = {2018}
}
Comments
16 pages; flow polynomial reciprocity added; title changed