Geodesic
Order polynomials and Pólya's enumeration theorem.
Katharina Jochemko1
1Freie Universität Berlin
The electronic journal of combinatorics, Tome 21 (2014) no. 2
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Pólya’s enumeration theorem states that the number of labelings of a finite set 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.
DOI : 10.37236/4066
Classification : 06A07, 06A11, 05A19, 05C15, 05C31, 05E18
Mots-clés : Pólya enumeration, group actions, partially ordered sets, order preserving maps, graph colorings

Katharina Jochemko  1

1 Freie Universität Berlin 
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     title = {Order polynomials and {P\'olya's} enumeration theorem.},
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Katharina Jochemko. Order polynomials and Pólya's enumeration theorem.. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/4066

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