The aim of this note is to show how existing product constructions for cyclic and 1-rotational block designs can be adapted to provide a highly effective method of obtaining product theorems for whist tournaments.
Academic Press
Let h(m) denote the class number of the quadratic field Q(√m). In this paper necessary and sufficient conditions for h (m) to be divisible by 16 are determined when m = −p, where p is a prime congruent to 1 modulo 8, and when m = −2p, where p is a prime congruent to ±1 modulo 8.
ABSTRACT. The cyclotomic numbers of order seven are given in terms of the solutions of a certain system of three quadratic diophantine equations.This is analogous to L. E. Dickson's evaluation of the cyclotomic numbers of order five, and is a convenient approach for applications to the theory of power residues.
Starters with adders, in abelian groups of odd order, have been used widely in recent combinatorial constructions, most notably in the study of Room squares. In this paper, constructions of adders for the so-called “patterned starter” are described, for a large class of nonabelian groups of odd order.
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