On divisibility for the permanents of $(\pm1)$-matrices

The classical results by Kräuter and Seifter concerning the divisibility of permanents for $(\pm1)$-matrices by large powers of $2$ are useful in testing whether the permanent is a nonvanishing function. In this paper, a new approach to this problem, which allows one to obtain a short combinatorial proof of the results by Kräuter and Seifter, is suggested.