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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.

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Correspondence to Richard Ehrenborg or Stephanie van Willigenburg.

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Ehrenborg, R., van Willigenburg, S. Enumerative Properties of Ferrers Graphs. Discrete Comput Geom 32, 481–492 (2004). https://doi.org/10.1007/s00454-004-1135-1

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Keywords

  • Computational Mathematic
  • Span Tree
  • Bipartite Graph
  • Symmetric Function
  • Hamiltonian Path