4 citations · 13 across the 8 of their papers we have counts for
8 papers · 1 filter
Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials)
Robert A. Proctor, Matthew J. Willis
Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and…
Convexity of tableau sets for type A Demazure characters (key polynomials), parabolic Catalan numbers
Robert A. Proctor, Matthew J. Willis
This is the first of three papers that develop structures which are counted by a "parabolic" generalization of Catalan numbers. Fix a subset R of {1,..,n-1}. Consider the ordered p…
Row bounds needed to justifiably express flagged Schur functions with Gessel-Viennot determinants
Robert A. Proctor, Matthew J. Willis
Let be a partition with no more than parts. Let be a weakly increasing -tuple with entries from . The flagged Schur function in the variables $x_1,…
Parabolic Catalan numbers count flagged Schur functions; Convexity of tableau sets for Demazure characters
Robert A. Proctor, Matthew J. Willis
Shuffles are n-multipermutations with suit multiplicities given by a subset R of {1,..,n-1}. Their inverses are ordered partitions of {1,..,n} whose block sizes derive from R. Thes…
Relating the type A alcove path model to the right key of a semistandard Young tableau, with Demazure character consequences
Matthew J. Willis
There are several combinatorial methods that can be used to produce type A Demazure characters (key polynomials). The alcove path model of Lenart and Postnikov provides a procedure…
New Descriptions of Demazure Tableaux and Right Keys, with Applications to Convexity
Matthew J. Willis
The right key of a semistandard Young tableau is a tool used to find Demazure characters for . This thesis gives methods to obtain the right and left keys by insp…
Semistandard Tableaux for Demazure Characters (Key Polynomials) and Their Atoms
Robert A. Proctor, Matthew J. Willis
The Schur function indexed by a partition lambda with at most n parts is the sum of the weight monomials for the Young tableaux of shape lambda. Let pi be an n-permutation. We give…
A Direct Way to Find the Right Key of a Semistandard Young Tableau
Matthew J. Willis
The right and left key of a semistandard Young tableau were introduced by Lascoux and Schutzenberger in 1990. Most prominently, the right key is a tool used to find Demazure charac…