Parallel Chip Firing Game Associated with n- cube Edges Orientations

We study the cycles generated by the chip firing game associated with n-cube orientations. We consider a particular class of partitions of vertices of n-cubes called left cyclic partitions that induce parallel periodic evolutions. Using this combinatorical model, we show that cycles generated by parallel evolutions are of even lengths from 2 to 2 on Hn (n ≥ 1), and of odd lengths different from 3 and ranging from 1 to 2n−1−1 on Hn (n ≥ 4). However, the question weather there exist parallel evolutions with period greater that 2 remains opened.