Motors and Impossible Firing Patterns in the Parallel Chip-Firing Game
نویسندگان
چکیده
منابع مشابه
Motors and Impossible Firing 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 contains much emergent complexity and has many connections to different areas of mathematics. In this work, we study firing sequences, which describe each vertex’s interaction with its neighbors in this game. First, we introduce the concepts of motors and motorized games....
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 کاملThe Chip Firing Game and Matroid Complexes
In this paper we construct from a cographic matroid M , a pure multicomplex whose degree sequence is the h–vector of the the matroid complex of M. This result proves a conjecture of Richard Stanley [Sta96] in the particular case of cographic matroids. We also prove that the multicomplexes constructed are M–shellable, so proving a conjecture of Manoj Chari [Cha97] again in the case of cographic ...
متن کاملParallel Chip Firing Game associated with n-cube orientations
We study the cycles generated by the chip firing game associated with n-cube orientations. We show the existence of the cycles generated by parallel evolutions of even lengths from 2 to 2n on Hn (n ≥ 1), and of odd lengths different from 3 and ranging from 1 to 2−1 on Hn (n ≥ 4).
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...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2015
ISSN: 0895-4801,1095-7146
DOI: 10.1137/130933770