2008/03/28 by Luc Lapointe, Lapointe, Luc, Yvan Le Borgne +3
Mathematics · #05A19 #05E05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A19 #msc:05E05
paper · pdf · doi:10.48550/arxiv.0803.4182
20 pages, 7 figures
arxiv created 2008/03/28 · openalex publication_date 2008/03/28 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We prove a previously conjectured 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.