Bijective Proofs for "Enumerative Properties of Ferrers Graphs"
Jason Burns
TL;DR
This paper provides bijective proofs for known enumerative formulas related to Ferrers graphs, specifically for counting spanning trees and Hamiltonian paths, enhancing combinatorial understanding.
Contribution
It introduces bijective proofs for existing formulas on Ferrers graphs' spanning trees and Hamiltonian paths, offering new combinatorial insights.
Findings
Bijective proofs for spanning tree counts
Bijective proofs for Hamiltonian path counts
Enhanced understanding of Ferrers graph properties
Abstract
Recently, Ehrenborg and Van Willenburg defined a class of bipartite graphs that correspond naturally to Ferrers diagrams, and proved several results about them. We give bijective proofs for the (already known) expressions for the number of spanning trees and (where applicable) Hamiltonian paths of these graphs. Their paper can be found at http://www.ms.uky.edu/~jrge/Papers/Ferrers_graphs.pdf .
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Graph theory and applications · Topological and Geometric Data Analysis