20200912, 03:25  #23  
Jan 2020
C_{16} Posts 
Quote:
Wikipedia has an useful paragraph about them (https://en.wikipedia.org/wiki/Permutation#Notations). If we want to arrange the numbers from 0 to 6 in descending order, we have: the oneline notation [6,5,4,3,2,1,0], the cycle notation (0,6)(1,5)(2,4)(3), but 1cycles like (3) are often omitted. For all RPS(n) games with n<=5, nontrivial automorphisms have exactly one cycle (more precisely, one ncycle), but this property doesn't hold in general. I guess it isn't spoiling to show the following RPS(7) game, far from being optimal: 0 > 1, 2, 3 1 > 4, 5, 6 2 > 1, 4, 5 3 > 1, 2, 6 4 > 0, 3, 6 5 > 0, 3, 4 6 > 0, 2, 5 It admits two nontrivial automorphisms: [2,4,5,1,3,0,6], or (0,2,5)(1,4,3)(6) [5,3,0,4,1,2,6], or (0,5,2)(1,3,4)(6) 

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