Hello,
I consider the permutations \sigma_i, where i\in \{1,\ldots,n\}, of the following kind:
\sigma_i is obtained by choosing the i-th element from (1,..,n) and by shifting it to the first position; for instance \sigma_3 = (3,1,2,\ldots,n). The parity of \sigma_i is clearly (-1)^{i-1}.
For...