Selected Papers in Combinatorics - a Volume Dedicated to R.G. Stanton

Professor Stanton has had a very illustrious career. His contributions to mathematics are varied and numerous. He has not only contributed to the mathematical literature as a prominent researcher but has fostered mathematics through his teaching and guidance of young people, his organizational skills and his publishing expertise. The following briefly addresses some of the areas where Ralph Stanton has made major contributions

Some perpendicular arrays for arbitrarily large t

AbstractWe show that perpendicular arrays exist for arbitrarily large t and with λ = 1. In particular, if d devides (t+1) then there is a PA1(t, t+1, t+(f(t+1)d)). If υ ≡ 1 or 2 (mod 3) then there is a PAλ(3, 4, υ) for any λ. If 3 divides λ then there is a PAλ(3, 4, υ) for any v. If n⩾2 there is a PA1(4, 5, 2n+1). Using recursive constructions we exhibit several infinite families of perpendicular arrays with t⩾3 and relatively small λ. We finally discuss methods of constructing perpendicular arrays based on automorphism groups. These methods allow the construction of PA's with (k−t)>1