A Novel Approach to Counting Perfect Matchings of Graphs

A Novel Approach to Counting Perfect Matchings of Graphs

We build a new perspective to count perfect matchings of a given graph. This idea is motivated by a construction on the relative cohomology group of surfaces. As an application of our theory, we reprove the celebrated Aztec Diamond theorem, and show how alternating sign matrices naturally arises thr...

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Hauptverfasser: Paul, Pravakar, Saikia, Manjil P
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
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Beschreibung
Zusammenfassung:We build a new perspective to count perfect matchings of a given graph. This idea is motivated by a construction on the relative cohomology group of surfaces. As an application of our theory, we reprove the celebrated Aztec Diamond theorem, and show how alternating sign matrices naturally arises through this framework.
DOI:10.48550/arxiv.2408.10273