Per Alexandersson, James Haglund, George Wang
Published 2018-05-01Version 1
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.
Comments: 12 pages, 4 figures, to appear in FPSAC 2018 conference proceedings
Some conjectures on the Schur expansion of Jack polynomials
From quasi-symmetric to Schur expansions with applications to symmetric chain decompositions and plethysm
Cumulants of Jack symmetric functions and $b$-conjecture
![QR code for arXiv:1805.00511 [math.CO]](http://oss.arxitics.com/images/favicon.svg)