2 citations · 2 across the 7 of their papers we have counts for
7 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.…
Counting odd numbers in truncations of Pascal's triangle
Robert G. Donnelly, Molly W. Dunkum, Courtney George +1
A "truncation" of Pascal's triangle is a triangular array of numbers that satisfies the usual Pascal recurrence but with a boundary condition that declares some terminal set of num…
Move-minimizing puzzles and diamond-colored modular/distributive lattices
Robert G. Donnelly, Elizabeth A. Donovan, Molly W. Dunkum +1
The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain w…