A normalization formula for the Jack polynomials in superspace and an   identity on partitions
  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. 
Luc Lapointe, Yvan Le Borgne, Philippe Nadeau