14 citations · 29 across the 19 of their papers we have counts for
20 papers
Olry Terquem's forgotten problem
Robert G. Donnelly, Molly W. Dunkum, Rachel McCoy
`Terquem's problem' is a name given in the twentieth century to the problem of enumerating certain integer sequences whose entries alternate in parity. In particular, this problem…
Explicit constructions of some infinite families of finite-dimensional irreducible representations of the type and simple Lie algebras
Robert G. Donnelly, Molly W. Dunkum, Austin White
We construct every finite-dimensional irreducible representation of the simple Lie algebra of type whose highest weight is a nonnegative integer multiple of the do…
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.…
Unit shapes and a wealth of calculus problems
Robert G. Donnelly, Alexander F. Thome
For a given family of similar shapes, what we call a "unit shape" strongly analogizes the role of the unit circle within the family of all circles. Within many such families of sim…