2023/10/26 by Houcine Ben Dali, Dali, Houcine Ben
Mathematics · #05E05 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2310.17756
openalex publication_date 2023/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent work, Maciej Dołe\kga and the author have given a formula of the expansion of the Jack polynomial J(α)λ in the power-sum basis as a non-orientability generating series of bipartite maps whose edges are decorated with the boxes of the partition λ. We conjecture here a variant of this expansion in which we restrict the sum on maps whose edges are injectively decorated by the boxes of λ. We prove this conjecture for Jack polynomials indexed by 2-column partitions. The proof uses a mix of combinatorial methods and differential operator computations.