Order Polynomials and Pólya's Enumeration Theorem
Keyword(s):
Set Up
◽
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.
2016 ◽
Vol 17
(2)
◽
pp. 1-35
◽
Keyword(s):
2012 ◽
Vol 137
(1-2)
◽
pp. 27-35
◽
1990 ◽
Vol 54
(1)
◽
pp. 123-128
◽