Balancing vectors in the max norm
Combinatorica
Disks, balls, and walls: analysis of a combinatorial game
American Mathematical Monthly
Games on line graphs and sand piles
Theoretical Computer Science
Structure of some sand piles model
Theoretical Computer Science
The structure of a linear chip firing game and related models
Theoretical Computer Science
RP'12 Proceedings of the 6th international conference on Reachability Problems
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We study some particular families of integer partitions called "sand piles" which are discrete dynamical systems. Our aim is to link these objects with the theory of partitions in order to enumerate them. We first consider the Ice Pile model IPM(k). We compute explicit asymptotic bounds for the number of sand piles in IPM(k) with area n. We then give the area, width and height generating functions. All these results are derived using bijections and q-equations. We then consider another model called L(θ).