International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 2, Pages 251-260
doi:10.1155/S0161171279000235
The four known biplanes with k=11
1Department of Mathematics, Lafayette College, Easton 18042, Pennsylvania, USA
2Department of Mathematics, Villanova University, Villanova 19085, Pennsylvania, USA
Received 21 May 1978
Copyright © 1979 Chester J. Salwach and Joseph A. Mezzaroba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The four known biplanes of order 9(k=11) are described in terms of their ovals, λ-chain structures, and automorphism groups. An exhaustive computer search for all biplanes of order 9 with certain chain structures has produced but two, one of which is new. None of these four biplanes yield the putative plane of order 10.