Cyclic Incidence Matrices

Abstract

Let it be required to arrange v elements into v sets such that each set contains exactly k distinct elements and such that each pair of sets has exactly λ elements in common (0 < λ < k < v). This problem we refer to as the v, k,λ combinatorial problem.

Difference sets in a finite group

“…Then, by (4.6), (4.7), SST has n+~Kw down the main diagonal and Xw elsewhere. Equation (4.8) now follows from the lemma of Hall and Ryser [7]. [7].…”

“…Then the automorphism x->xp is a multiplier of (6) Cf. Theorem 3.1 and Example 4 of Hall and Ryser [7].…”

“…Equation (4.8) now follows from the lemma of Hall and Ryser [7]. [7]. If G is abelian, e can be any odd divisor of v. If t> is even, n is a square (Chowla and Ryser [5]) and (4.…”

Variants of cyclic difference sets

“…Let e^l be a pth root of unity. Then following [4] we let Since D2 is a near difference set of type 2 we have…”

“…Then the incidence matrix The following nonexistence theorem for near difference sets of type 2 uses certain ideas developed earlier in [4] for cyclic difference sets. has a solution in integers x, y, and z, not all zero.…”