Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2

R Shaw, NA Gordon, JG Maks

Research output: Contribution to journalArticleScientificpeer-review


We consider the following `even hyperplane construction¿ of flats in the projective space which are external to the Grassmannian of lines of PG(4,2). Let the Grassmann image in of a partial spread in PG(4,2) be . Then is an r-cap on . Using the recent classification [N.A. Gordon, R. Shaw, L.H. Soicher, Classification of Partial Spreads in PG(4,2), pp. 63, available from:] of partial spreads in PG(4,2), we determine those partial spreads such that the projective space generated by the points mijmi+mj is an external flat. We show that, in this simple manner, we may construct seven out of the ten GL(5,2)-orbits of external flats. Keywords: Grassmannian G1,4,2; Partial spreads; External flats; GL(5,2)-orbits
Original languageUndefined/Unknown
Pages (from-to)137-146
Number of pages10
JournalDiscrete Mathematics
Issue number1
Publication statusPublished - 2005


  • academic journal papers
  • ZX CWTS JFIS < 1.00

Cite this