A Normalization Formula for the Jack Polynomials in Superspace and an Identity on Partitions
Copyright policy )A Normalization Formula for the Jack Polynomials in Superspace and an Identity on Partitions
We prove a conjecture of Desrosiers, Lapointe and Mathieu giving a closed form formula for the norm of the Jack polynomials in superspace with respect to a certain scalar product. The proof is mainly combinatorial and relies on the explicit expression in terms of admissible tableaux of the non-symmetric Jack polynomials. In the final step of the proof appears an identity on weighted sums of partitions that we demonstrate using the methods of Gessel-Viennot.
- University of Talca Chile
- University of Vienna Austria
- Laboratoire Bordelais de Recherche en Informatique France
identity on partitions, 05A19; 05E05, Symmetric functions and generalizations, Combinatorial aspects of partitions of integers, Exact enumeration problems, generating functions, Hypergeometric functions, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Commutation relations and statistics as related to quantum mechanics (general), 05A19, superpartitions, dominance order, 05E05, FOS: Mathematics, Mathematics - Combinatorics, symmetric functions, weighted sums of partitions, Combinatorics (math.CO), Jack polynomials, Gessel-Viennot, superspace, Combinatorial identities, bijective combinatorics
identity on partitions, 05A19; 05E05, Symmetric functions and generalizations, Combinatorial aspects of partitions of integers, Exact enumeration problems, generating functions, Hypergeometric functions, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Commutation relations and statistics as related to quantum mechanics (general), 05A19, superpartitions, dominance order, 05E05, FOS: Mathematics, Mathematics - Combinatorics, symmetric functions, weighted sums of partitions, Combinatorics (math.CO), Jack polynomials, Gessel-Viennot, superspace, Combinatorial identities, bijective combinatorics
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