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Algebraic and combinatorial isomorphisms of coherent configurations
by
Mikhail Klin
Ben-Gurion University of the Negev, Israel
Coauthors: Christian Pech (Dresden)
A coherent configuration H is a relational structure which consists of a finite set X and of a partition of the cartesian square of X, which satisfy a few natural axioms, imitating most important properties of 2-orbits (in a sense of H.Wielandt) of a permutation group acting on the set X. We define algebraic and (weak and strong) combinatorial isomorphisms and automorphisms of coherent configurations. The group Aut(H) of strong combinatorial automorphisms of H is its classical automorphism group. The group of weak combinatorial automorphisms of H coincides with the normalizer of Aut(H) in the symmetric group of the set X. A few algorithmic ideas are discussed which in some cases help to simplify the computation of the normalizer of a 2-closed permutation group.
Date received: January 29, 2001
Copyright © 2001 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 # cafo-66.