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Factorial Schur Functions and the Yang-Baxter Equation
Yang-Baxter Equation Factorial Schur Functions
2015/7/6
Factorial Schur functions are generalizations of Schur functions that have, in
addition to the usual variables, a second family of \shift" parameters. We show that a
factorial Schur function times a...
Proof of a Positivity Conjecture on Schur Functions
symmetric function Schur function multiplier sequence totally positive sequence
2014/6/3
In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let (t)n denote the rising factorial, and let ΛR denote the a...
Expansion of $k$-Schur functions for maximal $k$-rectangles within the affine nilCoxeter algebra
$k$-Schur functions $k$-rectangles affine nilCoxeter algebra Combinatorics
2011/9/14
Abstract: We give several explicit combinatorial formulas for the expansion of $k$-Schur functions indexed by maximal $k$-rectangles, $s_R^{(k)}$, in terms of the standard basis of the affine nilCoxet...
Using Hook Schur Functions to Compute Matrix Cocharacters
Using Hook Schur Functions Compute Matrix Cocharacters
2010/11/12
We use hook Schur functions to compute trace cocharacters of matrices in hooks. As an example we compute the cocharacters of 3 x 3 matrices in the one by two hook
Multiplicity-free skew Schur functions with interval support
Skew Schur functions Littlewood–Richardson coefficients multiplicity–free
2010/12/9
It is known that the Schur expansion of a skew Schur function runs over the interval of partitions, equipped with dominance order, defined by the least and the most dominant Littlewood-Richardson fill...
On the calculation of inner products of Schur functions
Group theory Group Representation theory Symmetric group
2010/6/30
Two methods for calculating inner products of Schur functions in terms of outer products and plethysms are given and they are easy to implement on a machine. One of these is derived from a recent anal...