Journal of Combinatorial Designs最新文献

In this article, we study symmetric designs admitting flag-transitive, point-imprimitive almost simple automorphism groups with socle sporadic simple groups. As a corollary, we present a classification of symmetric designs admitting flag-transitive automorphism group whose socle is a sporadic simple group, and in conclusion, there are exactly seven such designs, one of which admits a point-imprimitive automorphism group and the remaining are point-primitive.

It is shown that the flag-transitive, point-primitive automorphism groups of 2-$��\left(�\; ��v�\; �,�\; �k�\; �,�\; �\lambda ��\; �\right)�$ designs with $��\lambda �$ prime must be of affine type or almost simple type.

Let $�\; ��D�\; �=�\; ��\left(�\; ��P�\; �,�\; �ℬ��\; �\right)��$ be a nontrivial symmetric $�\; ���\left(�\; ��v�\; �,�\; �k�\; �,�\; �\lambda ��\; �\right)��$-design with $�\; ��\lambda �\; �\le �\; �100�$, and let $�\; ��G�$ be a flag-transitive automorphism group of $�\; ��D�$. In this paper, we show that if $�\; ��G�$ is quasiprimitive on $�\; ��P�$, then $�\; ��G�$ is of holomorph affine or almost simple type. Moreover, if $�\; ��G�$ is imprimitive on $�\; ��P�$, then $�\; ��G�$ is of almost simple type. According to this observation and to the classification of the finite simple groups we determine all such symmetric designs and the corresponding automorphism groups. We conclude with two open problems and a conjecture.

In this paper, we give a solution to the last outstanding case of the directed Oberwolfach problem with tables of uniform length. Namely, we address the two-table case with tables of equal odd length. We prove that the complete symmetric digraph on $��2�m�$ vertices, denoted $��K_{�2�m�}^{*}�$, admits a resolvable decomposition into directed cycles of odd length $��m�$. This completely settles the directed Oberwolfach problem with tables of uniform length.

Xu characterized rank 4 self-dual association schemes inducing three partial geometric designs by their character tables. We construct such association schemes as Schur rings over Abelian 2-groups.

Let $��S�$ be a finite proper partial geometry pg$���\left(��s�\; �,�\; �t�\; �,�\; �\alpha ��\; �\right)��$ not isomorphic to the van Lint–Schrijver partial geometry pg$���\left(��5�\; �,�\; �5�\; �,�\; �2��\; �\right)��$ and let $��G�$ be a group of automorphisms of $��S�$ acting primitively on both points and lines of $��S�$, we show that if $��\alpha �\; �\le �\; �60�$ then $��G�$ must be almost simple.