2020/08/14 by Blokhuis, Aart, De Boeck, Maarten, D'haeseleer, Jozefien
#05B25 #51E20 #51E23 #51E30 #52E14 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2008.06372
A t-intersecting constant dimension subspace code C is a set of k-dimensional subspaces in a projective space PG(n,q), where distinct subspaces intersect in a t-dimensional subspace. A classical example of such a code is the sunflower, where all subspaces pass through the same t-space. The sunflower bound states that such a code is a sunflower if |C| > ( \frac qk + 1 - qt + 1q - 1 )2 + ( \frac qk + 1 - qt + 1q - 1 ) + 1. In this article we will look at the case t=0 and we will improve this bound for q≥ 9: a set S of k-spaces in PG(n,q), q≥ 9, pairwise intersecting in a point is a sunflower if |S|> (\frac2√[6]q+\frac4√[3]q-(5)/(√(q)))(\frac qk + 1 - 1q - 1)2.