Séminaire Lotharingien de Combinatoire, B19i (1988).
[Formerly: Publ. I.R.M.A. Strasbourg, 1988, 361/S-19, p. 97-103.]

Norma Zagaglia Salvi

On the Permanent of Certain Submatrices of Circulant (0,1)-Matrices

Abstract. Let A = In + Ph + Pk, where P represents the permutation (1 2 ... n) and 1 <= h < k <= n-1. We prove that the submatrix of A obtained by deleting the rows and the columns intersecting at three non-zero entries belonging to I, Ph, Pk has positive permanent, except in certain cases that are completely determined.

The topic of this article is partially contained in the paper "On certain generalized circulant matrices," Mathematica Pannonica 14 (2003), 273-281, written jointly with Ernesto Dedó and Alberto Marini. Another article is in preparation.