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arXiv · 1810.12763

Some conjectures on the Schur expansion of Jack polynomials

Per Alexandersson·James Haglund·George Wang
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Abstract

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.

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Per Alexandersson, James Haglund, George Wang. 2018-10-26. Some conjectures on the Schur expansion of Jack polynomials. https://doi.org/10.4310/joc.2021.v12.n2.a2

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