MathDB
Permutations

Source: APMO 2000

April 1, 2006
inductionLaTeXcombinatorics unsolvedcombinatorics

Problem Statement

Given a permutation (a0,a1,…,ana_0, a_1, \ldots, a_n) of the sequence 0,1,…,n0, 1,\ldots, n. A transportation of aia_i with aja_j is called legal if ai=0a_i=0 for i>0i>0, and ai−1+1=aja_{i-1}+1=a_j. The permutation (a0,a1,…,ana_0, a_1, \ldots, a_n) is called regular if after a number of legal transportations it becomes (1,2,…,n,01,2, \ldots, n,0). For which numbers nn is the permutation (1,n,n−1,…,3,2,01, n, n-1, \ldots, 3, 2, 0) regular?
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