Year: 2013
Type: preprint
Abstract: Pólya's enumeration theorem is concerned with counting labeled sets up to symmetry. Given a finite group acting on a finite set of labeled elements it states that the number of labeled sets up to symmetry is given by a polynomial in the number of labels. We give a new perspective on this theorem by generalizing it to partially ordered sets and order preserving maps. Further we prove a reciprocity statement in terms of strictly order preserving maps generalizing a classical result by Stanley (1970). We apply our results to counting graph colorings up to symmetry.
Source: arXiv (Cornell University)
Author: Jochemko, Katharina
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1802849989