Rakotondrajao

1 Euler’s difference table and maximum permanents of (0, 1)-matrices

By Fanja Rakotondrajao.

First, we will enumerate the injections from [m] to [n] without k-fixed-points, that is, injection f without i such that f(i) = i+k. We will deduce the exact values of maximum permanent of (0, 1)−m×n matrices having m−k numbers of zero entries for any non negative integers 0 ≤ k ≤ m ≤ n. Unexpectedly these values are related to the numbers d_{n}^{k} of k-fixed-points-permutations over [n]. The numbers d_{n}^{k} are the derivate of Euler’s difference table.