Trees, forests and jungles: a botanical garden for cluster expansions
A. Abdesselam, V. Rivasseau
TL;DR
This paper introduces new combinatoric proofs and extensions for cluster expansion formulas, enhancing their theoretical foundation and demonstrating their application through educational examples.
Contribution
It provides novel combinatoric proofs and extends existing tree formulas for cluster expansions, with practical testing on pedagogical examples.
Findings
New combinatoric proofs for cluster expansions
Extensions of Brydges and Kennedy's tree formulas
Validated methods through pedagogical examples
Abstract
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and test them on a series of pedagogical examples.
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