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- Robert G. Donnelly
- J. Comb. Theory, Ser. A
- 1999

The numbers game is a one-player game played on a finite simple graph with certain " amplitudes " assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at the nodes using the amplitudes in a certain way. Combinatorial reasoning is used to show that those connected graphs… (More)

Let L be a complex semisimple Lie algebra with specified Chevalley generators. Let V be a finite dimensional representation of L with weight basis B. The supporting graph P of B is defined to be the directed graph whose vertices are the elements of B and whose colored edges describe the supports of the actions of the Chevalley generators on V . Four… (More)

- Robert G. Donnelly, Scott J. Lewis, Robert Pervine
- Discrete Mathematics
- 2003

- Robert G. Donnelly
- Eur. J. Comb.
- 2008

The numbers game is a one-player game played on a finite simple graph with certain " amplitudes " assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at the nodes using the amplitudes in a certain way. This game and its interactions with Coxeter/Weyl group theory and Lie… (More)

- L. Wyatt Alverson, Robert G. Donnelly, +4 authors N. J. Wildberger
- SIAM J. Discrete Math.
- 2009

For a rank two root system and a pair of nonnegative integers, using only elementary com-binatorics we construct two posets. The constructions are uniform across the root systems We then form the dis-tributive lattices of order ideals of these posets. Corollary 5.4 gives elegant quotient-of-products expressions for the rank generating functions of these… (More)

- L. Wyatt Alverson, Robert G. Donnelly, Scott J. Lewis, Robert Pervine
- Electr. J. Comb.
- 2006

We associate one or two posets (which we call " semistandard posets ") to any given irreducible representation of a rank two semisimple Lie algebra over C. Elsewhere we have shown how the distributive lattices of order ideals taken from semis-tandard posets (we call these " semistandard lattices ") can be used to obtain certain information about these… (More)

- Robert G. Donnelly, Scott J. Lewis, Robert Pervine
- Discrete Mathematics
- 2006

Results are obtained concerning the roots of asymmetric geometric representations of Coxeter groups. These representations were independently introduced by Vinberg and Eriksson, and generalize the standard geometric representation of a Coxeter group in such a way as to include all Kac–Moody Weyl groups. In particular, a characterization of when a… (More)

The numbers game is a one-player game played on a finite simple graph with certain " amplitudes " assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at the nodes using the amplitudes in a certain way. This game and its interactions with Coxeter/Weyl group theory and Lie… (More)