Résumé : Using a probabilistic approach proposed by Vershik, one can study various classes of integer partitions. By endowing those classes with the Boltzmann distribution and applying local limit theorems, one may derive asymptotic enumeration formulas (such as the Hardy–Ramanujan formula), or the shape of partitions of large integers (e.g. the curve derived by Temperley in 1952). After reminding some notions of combinatorics and the definition of the Boltzmann distribution over a combinatorial structure, we will explain a procedure that can be used in order to derive the kind of results we mentioned and we will discuss applications to some classes of partitions.
| Dernière modification : Monday 27 May 2024 |
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