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Let n21. For each me(1,..,n), define omeS2n as follows. For each ke(1,..2m), define m(k)=(k+1)/2 if k is odd, and om(k)=m+k/2 if k is even.

 


Let n21. For each me(1,..,n), define omeS2n as follows. For each ke(1,..2m), define m(k)=(k+1)/2 if k is odd, and om(k)=m+k/2 if k is even. 1. Determine inv(on), i.e. determine all inversions of n, and prove a closed formula for linv(on)). 2. For m22, express m as a product of an m-cycle and m-1.

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