Convergent and divergent numbers games for certain collections of edge-weighted graphs

Details Convergent and divergent numbers games for certain collections of edge-weighted graphs Convergent and divergent numbers games for certain collections of edge-weighted graphs

2008-10-29

arxiv.org/abs/0810.5362v1

Mathematics

Combinatorics

24 pages, results support a companion paper

Scientific paper

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 methods are used to investigate the convergence and divergence of numbers games played on certain such graphs. The results obtained here provide support for results in a companion paper.

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