Bivariate Order Polynomials
Copyright policy )Bivariate Order Polynomials
Motivated by Dohmen-P��nitz-Tittmann's bivariate chromatic polynomial $��_G(x,y)$, which counts all $x$-colorings of a graph $G$ such that adjacent vertices get different colors if they are $\le y$, we introduce a bivarate version of Stanley's order polynomial, which counts order preserving maps from a given poset to a chain. Our results include decomposition formulas in terms of linear extensions, a combinatorial reciprocity theorem, and connections to bivariate chromatic polynomials.
8 pages, 3 figures
- University of California, Berkeley United States
- San Francisco State University United States
- Millsaps College United States
- College of Alameda United States
Combinatorics of partially ordered sets, bivariate chromatic polynomial, Coloring of graphs and hypergraphs, Graph polynomials, acyclic orientation, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, bivariate order polynomial, order preserving map, Combinatorics (math.CO), combinatorial reciprocity theorem
Combinatorics of partially ordered sets, bivariate chromatic polynomial, Coloring of graphs and hypergraphs, Graph polynomials, acyclic orientation, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, bivariate order polynomial, order preserving map, Combinatorics (math.CO), combinatorial reciprocity theorem
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