14 citations · 25 across the 8 of their papers we have counts for
4 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…
d-Complete posets: local structural axioms, properties, and equivalent definitions
Robert A. Proctor, Lindsey M. Scoppetta
Although d-complete posets arose along the interface between algebraic combinatorics and Lie theory, they are defined using only requirements on their local structure. These posets…
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,…