Brandon Humpert

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The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite graphs and whose Hopf product and coproduct admit simple combinatorial descriptions. We give a new formula for the antipode in the graph algebra in terms of acyclic orientations; our formula contains many fewer terms than(More)
The chromatic symmetric function XG of a graph G was introduced by Stanley. In this paper we introduce a quasisymmetric generalization X G called the k-chromatic quasisymmetric function of G and show that it is positive in the fundamental basis for the quasisymmetric functions. Following the specialization of XG to χG(λ), the chromatic polynomial, we also(More)
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