Robert G. Donnelly

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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)
We further develop Eriksson’s theory of geometric representations of a Coxeter group with respect to certain possibly asymmetric bilinear forms, and we show how certain aspects of the geometry, though different from the standard (symmetric) case, can be fairly well behaved. In particular, we relate the finiteness of certain sets of roots to a combinatorial(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. Here, the edge amplitudes will be negative integers. Combinatorial(More)