14 citations · 25 across the 8 of their papers we have counts for
9 papers
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,…
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…
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…
d-Complete Posets Generalize Young Diagrams for the Jeu de Taquin Property
Robert A. Proctor
The jeu de taquin process produced a standard Young tableau from a skew standard Young tableau by shifting its entries to the northwest. We generalize this process to posets: certa…
Distributive lattices defined for representations of rank two semisimple Lie algebras
L. Wyatt Alverson, Robert G. Donnelly, Scott J. Lewis +4
For a rank two root system and a pair of nonnegative integers, using only elementary combinatorics we construct two posets. The constructions are uniform across the root systems A1…
Let's Expand Rota's Twelvefold Way For Counting Partitions!
Robert A. Proctor
Rota's Twelvefold Way gave formulas for the numbers of partitions which could be formed in twelve scenarios. This proposed AMM article expands Rota's 4 x 3 table. The resulting 6 x…