English

Projective Rectangles: A New Kind of Incidence Structure

Combinatorics 2024-07-17 v3

Abstract

A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial Desargues's theorem, a construction from projective planes, and alternative formulations. In sequels we study harmonic conjugation and the graphs of lines and subplanes.

Keywords

Cite

@article{arxiv.2307.04079,
  title  = {Projective Rectangles: A New Kind of Incidence Structure},
  author = {Rigoberto Florez and Thomas Zaslavsky},
  journal= {arXiv preprint arXiv:2307.04079},
  year   = {2024}
}

Comments

33 pp., 8 figures. V2: Major revisions, corrections, new title; 41 pp., 15 figures. V3: Rev. sects. 1 & 6; 40 pp., 15 figures

R2 v1 2026-06-28T11:25:16.224Z