Arithmetic of marked order polytopes, monotone triangle reciprocity, and partial colorings
Combinatorics
2014-07-21 v3 Metric Geometry
Abstract
For a poset P, a subposet A, and an order preserving map F from A into the real numbers, the marked order polytope parametrizes the order preserving extensions of F to P. We show that the function counting integral-valued extensions is a piecewise polynomial in F and we prove a reciprocity statement in terms of order-reversing maps. We apply our results to give a geometric proof of a combinatorial reciprocity for monotone triangles due to Fischer and Riegler (2011) and we consider the enumerative problem of counting extensions of partial graph colorings of Herzberg and Murty (2007).
Keywords
Cite
@article{arxiv.1206.4066,
title = {Arithmetic of marked order polytopes, monotone triangle reciprocity, and partial colorings},
author = {Katharina Jochemko and Raman Sanyal},
journal= {arXiv preprint arXiv:1206.4066},
year = {2014}
}
Comments
17 pages, 10 figures; V2: minor changes (including title); V3: examples included (suggested by referee), to appear in "SIAM Journal on Discrete Mathematics"