Geodesic
A normalization formula for the Jack polynomials in superspace and an identity on partitions
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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.
DOI : 10.37236/159
Classification : 05E05, 05A15, 05A19, 05A17, 33Cxx, 33D52, 81S05
Mots-clés : symmetric functions, superspace, Jack polynomials, superpartitions, dominance order, identity on partitions, Gessel-Viennot, weighted sums of partitions 
@article{10_37236_159,
     author = {Luc Lapointe and Yvan Le Borgne and Philippe Nadeau},
     title = {A normalization formula for the {Jack} polynomials in superspace and an identity on partitions},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/159},
     zbl = {1189.05172},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/159/}
}
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Luc Lapointe; Yvan Le Borgne; Philippe Nadeau. A normalization formula for the Jack polynomials in superspace and an identity on partitions. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/159

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