7 papers · 1 filter
A k-tableau characterization of k-Schur functions
Luc Lapointe, Jennifer Morse
We study k-Schur functions characterized by k-tableaux, proving combinatorial properties such as a k-Pieri rule and a k-conjugation. This new approach relies on developing the theo…
Order ideals in weak subposets of Young's lattice and associated unimodality conjectures
Luc Lapointe, Jennifer Morse
The k-Young lattice Y^k is a weak subposet of the Young lattice containing partitions whose first part is bounded by an integer k>0. The Y^k poset was introduced in connection with…
Schur function identities, their t-analogs, and k-Schur irreducibility
L. Lapointe, J. Morse
We obtain general identities for the product of two Schur functions in the case where one of the functions is indexed by a rectangular partition, and give their t-analogs using ver…
Schur function analogs for a filtration of the symmetric function space
L. Lapointe, J. Morse
We consider a filtration of the symmetric function space given by , the linear span of Hall-Littlewood polynomials indexed by partitions whose first part is not larger t…
The distributions of the entries of Young tableaux
Brendan D. McKay, Jennifer Morse, Herbert S. Wilf
Let T^* be a standard Young tableau of k cells. We show that the probability that a Young tableau of n cells contains T^* as a subtableau is, in the limit n -> \infty, equal to ν(π…
Tableaux statistics for two part Macdonald polynomials
L. Lapointe, J. Morse
The Macdonald polynomials expanded in terms of a modified Schur function basis have coefficients called the -Kostka polynomials. We define operators to build standard tableaux…