Some conjectures on the Schur expansion of Jack polynomials
Combinatorics
2026-02-17 v1
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.
Keywords
Cite
@article{arxiv.1810.12763,
title = {Some conjectures on the Schur expansion of Jack polynomials},
author = {Per Alexandersson and James Haglund and George Wang},
journal= {arXiv preprint arXiv:1810.12763},
year = {2026}
}
Comments
13 pages, 6 figures, full version of 2018 FPSAC extended abstract. arXiv admin note: substantial text overlap with arXiv:1805.00511