A 'Hot Potato' Gray Code for Permutations

نویسندگان

  • Xi Sisi Shen
  • Aaron Williams
چکیده

We give the n! permutations of [n] = {1,2, . . . , n} a cyclic order inspired by the children’s game of Hot Potato. Our order is a transposition Gray code, meaning that consecutive permutations differ by a single transposition. Furthermore, each transposition is restricted in two ways: (1) It must transpose value n (the “hot potato”); (2) It must transpose positions that are circularly adjacent or semi-adjacent. In other words, if each permutation is written circularly, then our order repeatedly transposes the value n with a value that is one or two positions to its left or right.

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عنوان ژورنال:
  • Electronic Notes in Discrete Mathematics

دوره 44  شماره 

صفحات  -

تاریخ انتشار 2013