On Graph Continued Fractions and the Heilmann-Lieb Theorem
Thom\'as Jung Spier
TL;DR
This paper provides a new proof of the Heilmann-Lieb Theorem using continued fractions inspired by Viennot's work on matching polynomials and branched continued fractions.
Contribution
It introduces a novel proof technique for the Heilmann-Lieb Theorem based on graph continued fractions and matching polynomial properties.
Findings
Proof of the Heilmann-Lieb Theorem using continued fractions
Connection between matching polynomials and branched continued fractions
New insights into graph polynomial structures
Abstract
Inspired by Viennot's observation that matching polynomials are numerators of branched continued fractions we present a proof of the Heilmann-Lieb Theorem.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Analytic Number Theory Research · History and Theory of Mathematics