Séminaire Lotharingien de Combinatoire, 78B.83 (2017), 12 pp.
Dun Qiu and Jeffrey B. Remmel
Schur Function Expansions and the Rational Shuffle Conjecture
Gorsky and Negut introduced operators Qm,n
on symmetric functions
and conjectured that, in the case where m and n are relatively
prime, the expansion of
in terms of the fundamental
quasi-symmetric functions are given by polynomials introduced by
Later Bergeron, Garsia, Leven, and Xin extended and refined the
conjectures of Gorsky and Negut to give a combinatorial interpretation
of the coefficients that arise in expansion of
terms of the fundamental
quasi-symmetric functions for arbitrary m and n which
we will call the rational shuffle conjecture. The rational shuffle
conjecture was later proved by Mellit in 2016. The main goal of this
to study the combinatorics of the coefficients that arise in the Schur
function expansion of
in the case where m or n
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
The following versions are available: