Character tables and the problem of existence of finite projective planes
Combinatorics
2017-09-20 v1 Representation Theory
Abstract
Recently, the authors of the present work (together with M. N. Kolountzakis) introduced a new version of the non-commutative Delsarte scheme and applied it to the problem of mutually unbiased bases. Here we use this method to investigate the existence of a finite projective plane of a given order d. In particular, a short new proof is obtained for the nonexistence of a projective plane of order 6. For higher orders like 10 and 12, the method is non decisive but could turn out to give important supplementary informations.
Keywords
Cite
@article{arxiv.1709.06149,
title = {Character tables and the problem of existence of finite projective planes},
author = {Máté Matolcsi and Mihály Weiner},
journal= {arXiv preprint arXiv:1709.06149},
year = {2017}
}