Divisibility by powers of $2$ of the permanents of multidimensional $(-1, 1)$-matrices

T. A. Asmus^ab, A. E. Guterman<sup>c

a</sup> Moscow Center for Fundamental and Applied Mathematics
^b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
^c Bar-Ilan University, Ramat Gan

Abstract: Let $\Omega(n, k)$ be a set of $k$-dimensional $(-1, 1)$-matrices of order $n$. This paper derives a new formula for computing multidimensional permanents of $(-1, 1)$-matrices. Using this formula, the divisibility of the permanents of multidimensional $(-1, 1)$ matrices by certain powers of $2$ is proved.

Key words and phrases: permanent, multidimensional matrices, $(-1, 1)$-matrices.

UDC: 512.643

Received: 28.10.2025