Values of the permanent function on $(0, 1)$- and $(-1, 0, 1)$-matrices

A. E. Guterman^a, D. A. Dryabin<sup>bc

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

Abstract: In this paper, the ranges of the permanent function on the sets of $(0, 1$)- and $(-1, 0, 1)$-matrices are discussed. A lower bound for the first non-realizable value of the permanent on the set of $(-1, 0, 1)$-matrices is obtained, and the bound for the $(0, 1)$-matrices is improved.

Key words and phrases: permanent, $(0, 1$)-matrices, $(-1, 0, 1)$-matrices.

UDC: 512.643

Received: 04.11.2025