2008/10/29 by Robert G. Donnelly, Donnelly, Robert G.
Mathematics · #05E15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E15
paper · pdf · doi:10.48550/arxiv.0810.5362
24 pages, results support a companion paper
arxiv created 2008/10/29 · arxiv updated 2009/12/01
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.