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A Note on Generalized Playfair Structures
by
Mark A. Miller
Marietta College
Let P and L be (not necessarily distinct) sets. Let I be a relation on P×L, and let IC be the complement of I in P×L. Let J be a relation on L×L. We say that S=(P, L, I, J) is a Generalized Playfair Structure provided the following axiom holds:
GPS Axiom: Given any (p, l) in IC, there exists a unique m in L such that (p, m) is in I and (l, m) is in J.
In this note we examine relationships between various combinatorial objects which give rise to Generalized Playfair Structures. Particular attention is given to affine planes and generalized quadrangles.
Date received: May 1, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawn-63.