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

doi:doi:10.1016/j.disc.2004.11.023

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

Discrete Mathematics and Optimization

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

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: http://www.hull.ac.uk/maths/people/rs/staffdetails.html] 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 language	Undefined/Unknown
Pages (from-to)	137-146
Number of pages	10
Journal	Discrete Mathematics
Volume	301
Issue number	1
DOIs	https://doi.org/doi:10.1016/j.disc.2004.11.023
Publication status	Published - 2005

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academic journal papers
ZX CWTS JFIS < 1.00

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

abstract = "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: http://www.hull.ac.uk/maths/people/rs/staffdetails.html] 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",

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T1 - Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2

AU - Shaw, R

AU - Gordon, NA

AU - Maks, JG

PY - 2005

Y1 - 2005

N2 - 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: http://www.hull.ac.uk/maths/people/rs/staffdetails.html] 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

AB - 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: http://www.hull.ac.uk/maths/people/rs/staffdetails.html] 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

KW - academic journal papers

KW - ZX CWTS JFIS < 1.00

U2 - doi:10.1016/j.disc.2004.11.023

DO - doi:10.1016/j.disc.2004.11.023

M3 - Article

SN - 0012-365X

VL - 301

SP - 137

EP - 146

JO - Discrete Mathematics

JF - Discrete Mathematics

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