Generalized chromatic polynomials

AbstractThere are several polynomials used in the study of combinatorics including Birkhoff's chromatic polynomial for graphs, Stanley's order polynomial for partially ordered sets, and Tutte's dichromatic polynomial for graphs. We develop a common basis for these polynomials which depends on a sequence of standard reference objects in the category under consideration, the sequence being called a chromatic complex. The values of the polynomial then indicate the number of morphisms in the category from the object in question to the objects in the chromatic complex