ИСТИНА

Permanent is a function which is similar to determinant by its definition but considerably different by its properties. Permanent of (0, 1)-matrices has an important role as a computing function in combinatorics. In this work we restrict our attention to the permanent function on (0, 1)-matrices only. In [1] it was proved that any fully indecomposable not convertible (0, 1)-matrix A of order n has at least 2n + 3 positive entries. In this talk we present the description of all such matrices with the minimal possible number of non-zero entries in matrix terms and in graph terms. Structure of fully indecomposable non-convertible (0, 1)-matrix with 2n + 3 positive elements is similar to sparse circulant matrices. Using this fact we compute permanent of all such matrices and show that these matri￾ces give a series of examples of non-convertible matrices which satisfy the conditions: a matrix can not be represented in upper block triangular form and a matrix has minimal possible permanent. [1] M. Budrevich, G. Dolinar, A.E. Guterman, B. Kuzma, Lower bounds for P´olya’s problem on permanent, nternational Journal of Algebra and Computation, 26 (6), 2016, 161–170