The four biplanes with k = 9
نویسندگان
چکیده
منابع مشابه
There are exactly five biplanes with k=11
A biplane is a 2-(k(k − 1)/2 + 1, k, 2) symmetric design. Only sixteen nontrivial biplanes are known: there are exactly nine biplanes with k < 11, at least five biplanes with k = 11, and at least two biplanes with k = 13. It is here shown by exhaustive computer search that the list of five known biplanes with k = 11 is complete. This result further implies that there exists no 3-(57, 12, 2) des...
متن کاملRank 3 Groups and Biplanes
Let G be a primitive rank 3 permutation group on a set X in which r(x) is a nontrivial G,-orbit, with II = I X 1, u = I I’(X)]. Tsuzuku [27] showed that, if G, acts as the symmetric group on r(x), then (v, n) = (2, 5), (3, lo), (5, 16), or (7, 50); he determined the possible groups in each case. Bannai [2] obtained essentially the same result under the assumption G, is 4-transitive on F(x). (Of...
متن کاملSplit Semi-Biplanes in Antiregular Generalized Quadrangles
There are a number of important substructures associated with sets of points of antiregular quadrangles. Inspired by a construction of P. Wild, we associate with any four distinct collinear points p, q, r and s of an antiregular quadrangle an incidence structure which is the union of the two biaffine planes associated with {p, r} and {q, s}. We investigate when this incidence structure is a sem...
متن کاملAn extremal problem related to biplanes
The existence problem for biplanes has proved to be intractable: only finitely many are known. However, it can be turned into an extremal problem, on which some progress can be made. A biplane is a set of subsets (blocks) of {I, ... , n} such that (a) any two blocks meet in two points; (b) any two points lie in two blocks. It is easy to see that, for some integer k, every block of a biplane con...
متن کاملExistence of near resolvable (v, k, k-1) BIBDs with k∈{9, 12, 16}
A necessary condition for existence of a (v, k, k−1) near resolvable BIBD is v ≡ 1 (mod k). In this paper, we update earlier known existence results when k ∈ {9, 12, 16}, and show this necessary condition is sufficient, except possibly for 26, 37 and 149 values of v for k = 9, 12, 16 respectively. Some new results for existence of (9, 8)-frames of type 9 are also obtained; in particular, we sho...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1978
ISSN: 0097-3165
DOI: 10.1016/0097-3165(78)90002-x