Geometry on the lines of spine spaces
Combinatorics
2017-04-21 v2
Abstract
Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with binary coplanarity relation, as well as with binary relation of being in one pencil of lines, is a sufficient system of primitive notions for these geometries. It is also shown that, over a spine space, the geometry of pencils of lines can be reconstructed in terms of the two binary relations.
Keywords
Cite
@article{arxiv.1612.01318,
title = {Geometry on the lines of spine spaces},
author = {K. Petelczyc and M. Żynel},
journal= {arXiv preprint arXiv:1612.01318},
year = {2017}
}