On Computer Modeling of Finite-generated Free Projective Planes

Abstract

This paper treats computer modeling of the process of constructing free projective planes — more precisely, to algorithmically finding their successive incidence matrices; and also to considering some numerical characteristics of these matrices. Matrix and bilinear forms approaches are used to study the growth rate of the number of new elements (points, lines) during step-by-step process of constructing projective plane starting with the Hall Pi^4 configuration. It appears that the number of new elements grows asymptotically as a double exponent (linear on log(log) scale.) Rough estimate from above also gives double exponential growth rate.