Some conjectures on the Schur expansion of Jack polynomials

26 Oct 2018  ·  Alexandersson Per, Haglund James, Wang George ·

We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards... These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases. read more

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Combinatorics