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Please join us on Friday for the thesis defense of Aidan McEnaney.

°Õ¾±³Ù±ô±ð:Ìý COMBINATORIAL RECIPROCITY FOR EQUIVARIANT CHROMATIC
POLYNOMIALS

´¡²ú²õ³Ù°ù²¹³¦³Ù:ÌýThe chromatic polynomial of a graph counts the number of ways in which the graph can be colored, with an input being the number of colors at hand. A combinatorial reciprocity theorem of Stanley’s tells us that evaluating the chromatic polynomial at -1 counts the number of acyclic orientations of the graph. Hanlon has proved an analogue of the aforementioned reciprocity theorem for the orbital chromatic polynomial, which counts colorings that differ by a rotation or symmetry as the same. In this thesis we establish a reciprocity theorem for a new family of chromatic polynomials, defined in terms of group representations, that generalizes both the standard and the orbital chromatic polynomials.