On evaluating permanents and a matrix of contangents∗
David Callan · Linear and Multilinear Algebra · 1995
The following equality is established: Let C denote the n-square matrix whose (i,j) entry is and let J denote the n-square matrix of 1′s. Then per A classical identity stated by R.F. Scott follows [As a matter of side interest, a case is presneted that Scott had done more than conjecture his identity]. Two standard methods for evaluting permanents and a third, apparently new, one are developed from the unified point of view of Möbius inversion. Our proof is based on the third one, and the resulting expression is simplified by counting weighted configurations of balls, cells and boxes. Standard manipulations complete the proof. A possible generalization is discussed.