English

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}
}