, Volume 32, Issue 4, pp 481-492

Enumerative Properties of Ferrers Graphs

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Abstract

We define a class of bipartite graphs that correspond naturally with Ferrers diagrams. We give expressions for the number of spanning trees, the number of Hamiltonian paths when applicable, the chromatic polynomial and the chromatic symmetric function. We show that the linear coefficient of the chromatic polynomial is given by the excedance set statistic.