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S(j)+S^(-1)(j)=n+1

Source: India tst 2006 p1

June 26, 2012
linear algebramatrixcombinatorics proposedcombinatorics

Problem Statement

Let nn be a positive integer divisible by 44. Find the number of permutations σ\sigma of (1,2,3,⋯ ,n)(1,2,3,\cdots,n) which satisfy the condition σ(j)+σ−1(j)=n+1\sigma(j)+\sigma^{-1}(j)=n+1 for all j∈{1,2,3,⋯ ,n}j \in \{1,2,3,\cdots,n\}.
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