Geodesic
Hyperoctahedral Eulerian idempotents, Hodge decompositions, and signed graph coloring complexes
Benjamin Braun1 ; Sarah Crown Rundell2
1University of Kentucky
2Denison University
The electronic journal of combinatorics, Tome 21 (2014) no. 2
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Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph $G$ are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for $G$. We prove a type B analogue of this result for chromatic polynomials of signed graphs using hyperoctahedral Eulerian idempotents.
DOI : 10.37236/3636
Classification : 05C15, 05C22, 18G35, 05C31
Mots-clés : chromatic polynomial, signed graph, Hodge decomposition, Eulerian idempotent, coloring complex

Benjamin Braun  1   ; Sarah Crown Rundell  2

1 University of Kentucky
2 Denison University 
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     author = {Benjamin Braun and Sarah Crown Rundell},
     title = {Hyperoctahedral {Eulerian} idempotents, {Hodge} decompositions, and signed graph coloring complexes},
     journal = {The electronic journal of combinatorics},
     year = {2014},
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Benjamin Braun; Sarah Crown Rundell. Hyperoctahedral Eulerian idempotents, Hodge decompositions, and signed graph coloring complexes. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/3636

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