2011/04/19 by Patrick Desrosiers, Luc Lapointe, Pierre Mathieu · 25 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Art #Art history #Computer science #Humanities #Library science #Mathematical functions and polynomials #Mathematics #Normalization (sociology) #Random Matrices and Applications #Social science #Sociology #math-ph #math.CO #math.MP #msc:05E05 #msc:33D52 #msc:81Q60
paper · pdf · doi:10.1093/imrn/rnr235
published in International Mathematics Research Notices 2012(23), 5267-5327 (Oxford University Press) · 42 pages, 10 figures. v2: minor corrections in Eqs (16) and (17)
arxiv created 2011/04/19 · openalex publication_date 2011/12/15 · arxiv updated 2012/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Two evaluation formulas are derived for the Jack superpolynomials. The evaluation formulas are expressed in terms of products of fillings of skew diagrams. One of these formulas is nothing but the evaluation formula of the Jack polynomials with prescribed symmetry, which thereby inherits here a very simple formulation. Among the auxiliary results required to establish the evaluation formulas, the determination of the conditions ensuring the nonvanishing coefficients in a Pieri-type rule for Jack superpolynomials is worth pointing out. An important application of the evaluation formulas is a new derivation of the combinatorial norm of the Jack superpolynomials. We finally mention that the introduction of a simpler version of the dominance ordering on superpartitions is fundamental to establishing our results.