Sequences and Functions Derived from Projective Planes and Their Difference Sets

2012 ◽  
pp. 64-80 ◽  
Author(s):  
Alexander Pott ◽  
Qi Wang ◽  
Yue Zhou
Keyword(s):  
Difference Sets ◽  
Projective Planes

A Class of Non-Desarguesian Projective Planes

1957 ◽  
Vol 9 ◽  
pp. 378-388 ◽  
Author(s):  
D. R. Hughes
Keyword(s):  
Positive Integer ◽  
Projective Plane ◽  
Collineation Group ◽  
Difference Sets ◽  
Projective Planes ◽  
Desarguesian Projective Plane ◽  
Desarguesian Plane ◽  
Desarguesian Projective Planes

In (7), Veblen and Wedclerburn gave an example of a non-Desarguesian projective plane of order 9; we shall show that this plane is self-dual and can be characterized by a collineation group of order 78, somewhat like the planes associated with difference sets. Furthermore, the technique used in (7) will be generalized and we will construct a new non-Desarguesian plane of order p2n for every positive integer n and every odd prime p.

scholarly journals On relative difference sets and projective planes

1974 ◽  
Vol 15 (2) ◽  
pp. 150-154 ◽  
Author(s):  
Fred Piper
Keyword(s):  
Permutation Group ◽  
Difference Sets ◽  
Projective Planes ◽  
Relative Difference ◽  
Permutation Representation ◽  
Hamiltonian Group ◽  
Relative Difference Sets

A permutation group is quasiregular if it acts regularly on each of its orbits (i.e. the stabiliser of an element fixes every other element in its orbit). So, in particular, any permutation representation of an abelian or hamiltonian group must be quasiregular.

Combinatorial Problems

1950 ◽  
Vol 2 ◽  
pp. 93-99 ◽  
Author(s):  
S. Chowla ◽  
H. J. Ryser
Keyword(s):  
Combinatorial Problem ◽  
Difference Sets ◽  
Projective Planes ◽  
Combinatorial Problems ◽  
Block Designs ◽  
Incomplete Block ◽  
Incidence Matrices ◽  
Finite Projective Planes ◽  
Balanced Incomplete Block Designs ◽  
Balanced Incomplete Block

Let it be required to arrange v elements into v sets such that every set contains exactly k distinct elements and such that every pair of sets has exactly elements in common . This combinatorial problem is studied in conjunction with several similar problems, and these problems are proved impossible for an infinitude of v and k. An incidence matrix is associated with each of the combinatorial problems, and the problems are then studied almost entirely in terms of their incidence matrices. The techniques used are similar to those developed by Bruck and Ryser for finite projective planes [3]. The results obtained are of significance in the study of Hadamard matrices [6;8], finite projective planes [9], symmetrical balanced incomplete block designs [2; 5], and difference sets [7].

Spiky projective planes

1991 ◽  
Vol 257 (1-2) ◽  
pp. 51-55
Author(s):  
D. Johnston
Keyword(s):  
Projective Planes

scholarly journals On submaximal curves in fake projective planes

2021 ◽  
Vol 225 (10) ◽  
pp. 106709
Author(s):  
Piotr Pokora ◽  
Halszka Tutaj-Gasińska
Keyword(s):  
Projective Planes
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