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November 2018 Mozes' Game of Numbers on Directed Graphs
Rohan Hemasinha, Avinash J. Dalal, Donald McGinn
Missouri J. Math. Sci. 30(2): 117-131 (November 2018). DOI: 10.35834/mjms/1544151689

Abstract

In 1986, the contestants of the $27$th International Mathematical Olympiad were given a game of numbers played on a pentagon. In 1987, Mozes generalized this game to an arbitrary undirected, weighted, connected graph. The convergence properties and total number of moves of any convergent game have been resolved by Mozes using Weyl groups. Eriksson provided an alternate proof using matrix theory and graph theory. In this paper, we briefly discuss the results of Mozes and Eriksson on undirected graphs. Then we generalize this game to arbitrary directed, strongly connected graphs and investigate the convergence properties of the game of numbers.

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Rohan Hemasinha. Avinash J. Dalal. Donald McGinn. "Mozes' Game of Numbers on Directed Graphs." Missouri J. Math. Sci. 30 (2) 117 - 131, November 2018. https://doi.org/10.35834/mjms/1544151689

Information

Published: November 2018
First available in Project Euclid: 7 December 2018

zbMATH: 07063848
MathSciNet: MR3884734
Digital Object Identifier: 10.35834/mjms/1544151689

Subjects:
Primary: 54A40

Rights: Copyright © 2018 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.30 • No. 2 • November 2018
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