14 citations · 29 across the 19 of their papers we have counts for
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Sign-alternating Gibonacci polynomials
Robert G. Donnelly, Molly W. Dunkum, Murray L. Huber +1
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the…
Symmetric Fibonaccian distributive lattices and representations of the special linear Lie algebras
Robert G. Donnelly, Molly W. Dunkum, Sasha V. Malone +1
We present a family of rank symmetric diamond-colored distributive lattices that are naturally related to the Fibonacci sequence and certain of its generalizations. These lattices…
Gelfand--Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions
Robert G. Donnelly, Molly W. Dunkum
We generalize the famous weight basis constructions of the finite-dimensional irreducible representations of obtained by Gelfand and Tsetlin in 1950.…
Analogs of Schur functions for rank two Weyl groups obtained from grid-like posets
L. Wyatt Alverson, Robert G. Donnelly, Scott J. Lewis +1
In prior work, the authors, along with M. McClard, R. A. Proctor, and N. J. Wildberger, studied certain distributive lattice models for the `Weyl bialternants' (aka `Weyl character…
Finite diamond-colored modular and distributive lattices with applications to combinatorial Lie representation theory
Robert G. Donnelly
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. S…
Poset models for Weyl group analogs of symmetric functions and Schur functions
Robert G. Donnelly
The `Weyl symmetric functions' studied here naturally generalize classical symmetric (polynomial) functions, and `Weyl bialternants,' sometimes also called Weyl characters, analogi…