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- Brandon Humpert, Jeremy L. Martin
- SIAM J. Discrete Math.
- 2012

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 com-binatorial 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)

- Brandon Humpert
- Electr. J. Comb.
- 2011

The chromatic symmetric function X G of a graph G was introduced by Stan-ley. In this paper we introduce a quasisymmetric generalization X k 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 X G to χ G (λ), the chromatic polynomial, we… (More)

- R. B. Abhyankar, B. Humpert
- SIGD
- 1988

As an example of a logic circuit design problem, we consider the two-inverter puzzle [1] which may be stated as follows:Using any number of AND, OR gates but no more than two NOT gates (inverters), design a logic circuit with three inputs i1, i2, i3 and three outputs o1, o2, 03 such that o1=NOT (il), o2=NOT (i2), o3=NOT (i3).

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