Percy Alexander MacMahon,
1911 Encyclopædia Britannica, Volume 6…
(1911)
“ We have to find the number of permutations such that exactly m of the letters are in places they originally occupied. We have the particular redundant product (ax1 + x2 + ... + xn) ξ1 (x1 + ax2 + ... + xn) ξ2 ... (x1 + x2 + ... + axn) ξn in which the sought number is the coefficient of am xξ11 xξ22 ... xξnn. The true generating function is derived from the determinant and has the form It is clear that a large class of problems in permutations can be solved in a similar manner, viz. by giving special values to the elements of the determinant of the matrix. ”
