Bounds on Minors of Binary Matrices

General Lower Bounds on Maximal Determinants of Binary Matrices

We prove general lower bounds on the maximal determinant of n× n {+1,−1}matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and Levin (2010) and, for certain congruence classes of n mod 4, the results of Koukouvinos, Mitrouli and Seberry (2000). In an Appendix we give a new proof, using Jacobi’s determinant identity, of a...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

A Technique for Computing Minors of Binary Hadamard Matrices and Application to the Growth Problem

A technique to compute all the possible minors of order n − j of binary Hadamard matrices with entries (0, 1) is introduced. The method exploits the properties of such matrices S and also the symmetry and special block structure appearing when one forms the matrix D D, where D is a submatrix of S. Theoretically, the method works for every pair of values n and j and provides general analytical f...

Counting 2-connected deletion-minors of binary matroids

We introduce a new invariant for a binary matroid and use it to obtain upper bounds on the number of circuits and, more generally, the number of 2-connected deletion minors containing a fixed element of the matroid. We conjecture that this invariant can also be used to bound the modulus of the roots of the matroid’s characteristic polynomial.

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...