Pairwise transitive 2-designs

ibn 2 - TRANSITIVE DESIGNS

2-Transitive and ag-transitive designs

Throughout this paper D always will denote a design with v points, k > 2 points per line, and = 1 line through any two diierent points. Let G Aut (D). I will primarily be interested in the case in which G either is 2-transitive on the points of D or is transitive on the ags (incident point-line pairs) of D. Note that 2-transitivity implies ag-transitivity since = 1. The subject matter has been ...

2 - Transitive and flag - transitive designs

Throughout this paper V always will denote a design with "t; points, k > 2 points per line, and>' = 1 line through any two different points. Let G <:: Aut (V). I will primarily be interested in the case in which G either is 2-transitive on the points of VOl' is transitive on the flags (incident point-line pairs) ofV. Note that 2-transitivity implies flag-transitivity since>. = 1. The subject ma...

Classification of 2-transitive symmetric designs

All symmetric designs are determined for which the automorphism group is 2-transitive on the set of points. This note contains a proof of the following result. Theorem. Let D be a symmetric design with v > 2k such that Aut D is 2-transitive on points. Then D is one o f the following: (i) a projective space; (ii) the unique Hadamard design with v = I 1 and k = 5; (iii) a unique design with v = 1...

Some Pairwise Balanced Designs

A pairwise balanced design, B(K; v), is a block design on v points, with block sizes taken from K, and with every pair of points occurring in a unique block; for a fixed K, B(K) is the set of all v for which a B(K; v) exists. A set, S, is a PBD-basis for the set, T , if T = B(S). Let Na(m) = {n : n ≡ a mod m}, and N≥m = {n : n ≥ m}; with Q the corresponding restriction of N to prime powers. Thi...