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Characterization of Balanced Coherent Configurations
Let be a group acting on a finite set . Then acts on
by its entry-wise action and its orbits form the basis
relations of a coherent configuration (or shortly scheme). Our concern is to
consider what follows from the assumption that the number of orbits of on
is constant whenever and are
orbits of on . One can conclude from the assumption that the
actions of on 's have the same permutation character and are
not necessarily equivalent. From this viewpoint one may ask how many
inequivalent actions of a given group with the same permutation character there
exist. In this article we will approach to this question by a purely
combinatorial method in terms of schemes and investigate the following topics:
(i) balanced schemes and their central primitive idempotents, (ii)
characterization of reduced balanced schemes
Strongly regular graphs induced by polarities of symmetric designs
Graphs;mathematics
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