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Rakotondrajao
%Fanja","frakoton@univ-antananarivo.mg","
\section{Euler's difference table and maximum permanents of $(0,1)$-matrices} By {\sl Fanja Rakotondrajao}.  

\medskip  \noindent 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 \times n $ matrices having $m-k$ numbers of zero entries for any non negative integers $0\leq k \leq m \leq n$. Unexpectedly these values are related to the numbers $d^k_n$ of $k$-fixed-points-permutations over $[n]$. The numbers $d^k_n$ are the derivate of Euler's difference table.
%$k$-fixed-points, $(0,1)$-matrices, permanent, injections, $k$-fixed-points-permutations.","05A19","05B20",01:10:34","Wed Jan 16 2008","196.192.40.118"
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