2013/10/02 by Katharina Jochemko, Jochemko, Katharina
Mathematics · #05A19 #05C15 #05C31 #05E18 #06A07 #06A11 #Advanced Combinatorial Mathematics #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.1310.0838
openalex publication_date 2013/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.