منابع مشابه
Sorting via Chip-Firing
We investigate a variant of the chip-firing process on the infinite path graph Z: rather than treating the chips as indistinguishable, we label them with positive integers. To fire an unstable vertex, i.e. a vertex with more than one chip, we choose any two chips at that vertex and move the lesser-labeled chip to the left and the greater-labeled chip to the right. This labeled version of the ch...
متن کامل18.204: Chip Firing Games
Chip firing is a one-player game where piles start with an initial number of chips and any pile with at least two chips can send one chip to the piles on either side of it. When all of the piles have no more than a single chip, the game ends. In this paper we review fundamental theorems related to this game on a two dimensional number line, including the fact that termination and final configur...
متن کاملFiring Patterns in the Parallel Chip-Firing Game
The parallel chip-firing game is an automaton on graphs in which vertices “fire” chips to their neighbors. This simple model, analogous to sandpiles forming and collapsing, contains much emergent complexity and has connections to different areas of mathematics including self-organized criticality and the study of the sandpile group. In this work, we study firing sequences, which describe each v...
متن کاملParallel Chip Firing on Digraphs
Given some multidigraph , a state is any dist ribut ion of some chips on its vert ices. We transform t his initial st ate step by step. Every vert ex checks whet her it is able to send one chip through every outgoing arc. If it can, it does; otherwise it does not send any chip. All vert ices check and send in parallel. Finally, at every vert ex all incoming chips are added to the remaining chip...
متن کاملChip-firing Games on Graphs
We analyze the following (solitaire) game: each node of a graph contains a pile of chips, and a move consists of selecting a node with at least as many chips on it as its degree, and let it send one chip to each of its neighbors. The game terminates if there is no such node. We show that the finiteness of the game and the terminating configuration are independent of the moves made. If the numbe...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2018
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-018-2159-1