arXiv subjects

R. J. Nowakowski

Publications and source records attributed to R. J. Nowakowski.

2 recordsLinked to original sources

arXiv2023

Infinitely many absolute universes

Absolute combinatorial game theory was recently developed as a unifying tool for constructive/local game comparison (Larsson et al. 2018). The theory concerns {\em parental universes} of combinatorial games; standard closure properties are satisfied and each pair of non-empty sets of forms of the universe makes a form of the universe. Here we prove that there is an infinite number of absolute misère universes, by recursively expanding the dicot misère universe and the dead-ending universe. On the other hand, we prove that normal-play has exactly two absolute universes, namely the full space, and the universe of all-small games.

math.CO↗

arXiv2018

A Variation on Chip-Firing: the diffusion game

We introduce a natural variant of the parallel chip-firing game, called the diffusion game. Chips are initially assigned to vertices of a graph. At every step, all vertices simultaneously send one chip to each neighbour with fewer chips. As the dynamics of the parallel chip-firing game occur on a finite set the process is inherently periodic. However the diffusion game is not obviously periodic: even if $2|E(G)|$ chips are assigned to vertices of graph G, there may exist time steps where some vertices have a negative number of chips. We investigate the process, prove periodicity for a number of graph classes, and pose some questions for future research.

cs.DM↗