Values of Minors of Some Infinite Families of Matrices Constructed from Supplementary Difference Sets and Their Application to the Growth Problem

Authors

C. Koukouvinos, National Technical University of Athens, Greece
M. Mitrouli, University of Athens, Greece
Jennifer Seberry, University of WollongongFollow

RIS ID

12895

Publication Details

This article was originally published as Koukouvinos, C, Mitrouli, M and Seberry, J, Values of Minors of Some Infinite Families of Matrices Constructed from Supplementary Difference Sets and Their Application to the Growth Problem, Linear Algebra and its Applications, 406, 2005, 218-234. Copyright Elsevier 2005. Original journal available here.

Abstract

We obtain explicit formulae for the values of the 2v - j minors, j = 0,1, 2 of (1, -1) matrices of order 2v, v odd, where the matrix is constructed using two circulant or type 1 incidence matrices of 2— {v; k1, k2, λ} sds. This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our theoretical formulae imply growth close to the order 2v but experimentation has not yet supported this result. An open problem remains to establish whether the (1, -1) CP incidence matrices of certain SBIBDs, can have growth greater than 2v.