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The classical results by Kräuter and Seifter concerning the divisibility of permanents for (±1)-matrices by large powers of 2 are useful in testing whether the permanent function is nonvanishing. This paper suggests a new approach to this problem, allowing one to obtain a short combinatorial proof of the results by Kräuter and Seifter. [ABSTRACT FROM AUTHOR]

Let $ \mathbb{F} $ be a finite field of characteristics different from 2. We show that no bijective map transforms the permanent to the determinant when the cardinality of $ \mathbb{F} $ is sufficiently large. Also we determine Gibson barriers (the maximal and minimal numbers of nonzero elements) for convertible (0 , 1)-matrices and solve several related problems in different matrix subspaces. Our results are illustrated by examples. This paper is based on the joint work with G. Dolinar, B. Kuzma, and M. Orel. [ABSTRACT FROM AUTHOR]

The study of multiple transitivity of products of sets of permutations on a set Ω is reduced to the study of products of matrices of small dimensions. For effective application of this approach we need some information about properties of equivalence relations defined on the Cartesian degree of the set Ω. These properties are studied for relations induced by various groups. [ABSTRACT FROM AUTHOR]