Robert A. Liebler

The rank 3 permutation representations of the finite classical groups

The permutation representations in the title are all determined, and no surprises are found to occur.

Certain distance-regular diagraphs and related rings of characteristic 4

Abstract An infinite family of distance-regular edge transitive digraphs of girth 4 is constructed using cyclotomic extensions of the integers modulo 4. Automorphism groups are computed and it is shown that nonisomorphic digraphs with the same parameters occur in some cases.

Antipodal Distance Transitive Covers of Complete Graphs

A distance-transitive antipodal cover of a complete graphKnpossesses an automorphism group that acts 2-transitively on the fibres. The classification of finite simple groups implies a classification of finite 2-transitive permutation groups, and this allows us to determine all possibilities for such a graph. Several new infinite families of distance-transitive graphs are constructed.

Antipodal Distance-transitive Covers of Complete Bipartite Graphs

This paper completes the classification of antipodal distance-transitive covers of the complete bipartite graphsKk,k,wherek?3.For such a cover the antipodal blocks must have sizer?k.Although the caser=khas already been considered, we give a unified treatment ofr?k.We use deep group-theoretic results as well as representation-theoretic data about explicit linear groups and group coset geometries.Apart from the generic examples arising from finite projective spaces, there are three sporadic examples (arising from the outer automorphisms of the symmetric groupS6and of the Mathieu groupM12and one related to non-abelian Singer groups onPG2(4))and an infinite family having solvable automorphism group (and with parametersr=qb, k=qa,where(qb-1)gcd(b,q-1)divides2a(q-1)andqis a prime power).

Combinatorial S >n -Modules as Codes

AbstractCertain

On the uniqueness of the tetrahedral association schemes

\mathbb{Z}S_n

Neighbour-transitive codes in Johnson graphs

-modules related to the kernels ofincidence maps between types in the poset defined by the natural productorder on the set of n-tuples with entries from {1,