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On the existence of a (2,3)-spread in V(7,2)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2016 (English)In: Ars combinatoria, ISSN 0381-7032, Vol. 124, 161-164 p.Article in journal (Refereed) PublishedText
Abstract [en]

An (s, t)-spread in a finite vector space V = V (n, q) is a collection F of t-dimensional subspaces of V with the property that every s-dimensional subspace of V is contained in exactly one member of F. It is remarkable that no (s, t)-spreads has been found yet, except in the case s = 1. In this note, the concept a-point to a (2,3)-spread F in V = V(7, 2) is introduced. A classical result of Thomas, applied to the vector space V, states that all points of V cannot be alpha-points to a given (2, 3)-spread.F. in V. In this note, we strengthened this result by proving that every 6-dimensional subspace of V must contain at least one point that is not an a-point to a given (2, 3)-spread of V.

Place, publisher, year, edition, pages
Charles Babbage Research Centre , 2016. Vol. 124, 161-164 p.
National Category
URN: urn:nbn:se:kth:diva-183339ISI: 000369773900012OAI: diva2:910075

QC 20160308

Available from: 2016-03-08 Created: 2016-03-07 Last updated: 2016-03-19Bibliographically approved

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Heden, Olof
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