Journal of Combinatorics
Volume 12 (2021)
Some conjectures on the Schur expansion of Jack polynomials
Pages: 215 – 233
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.
Jack polynomials, Schur polynomials, quasi-Yamanouchi tableaux, Eulerian numbers, Stirling numbers, Rook polynomials
2010 Mathematics Subject Classification
Primary 05E05. Secondary 05A15.
Per Alexandersson was partially supported by the Knut and Alice Wallenberg Foundation, James Haglund was partially supported by NSF grant DMS-1600670, and George Wang was partially supported by the NSF Graduate Research Fellowship, DGE-1321851.
Received 11 November 2018
Accepted 7 May 2020
Published 16 July 2021