Theory of linear and integer programming
Theory of linear and integer programming
Complex Systems
The &sgr;-game and cellular automata
American Mathematical Monthly
The mod p rank of incidence matrices for connected uniform hypergraphs
European Journal of Combinatorics - Special issue dedicated to Bernt Lindstro¨m
On the p-Rank of the Adjacency Matrices of Strongly Regular Graphs
Journal of Algebraic Combinatorics: An International Journal
σ-game, σ+-game and two-dimensional additive cellular automata
Theoretical Computer Science
Discrete Mathematics
Note: Minimum light number of lit-only σ-game on a tree
Theoretical Computer Science
A singular quartic curve over a finite field and the Trisentis game
Finite Fields and Their Applications
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We present a generalization of the so-called σ-game, introduced by Sutner (Math. Intelligencer 11 (1989) 49), a combinatorial game played on a graph, with relations to cellular automata, as well as odd domination in graphs. A configuration on a graph is an assignment of values in {0,...,p- 1} (where p is an arbitrary positive integer) to all the vertices of G. One may think of a vertex v of G as a button the player can press at his discretion. If vertex v is chosen, the value of all the vertices adjacent to v increases by 1 modulo p. This defines an equivalence relation between the configurations: two configurations are in relation if it is possible to reach one from the other by a sequence of such operations. We investigate the number of equivalence classes that a given graph has, and we give formulas for trees and special regular graphs.