Properties of sets of Subspaces with Constant Intersection Dimension

Lisa Hernandez Lucas, ,Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
2019 Advances in Mathematics of Communications  
A (k, k − t)-SCID (set of Subspaces with Constant Intersection Dimension) is a set of k-dimensional vector spaces that have pairwise intersections of dimension k − t. Let C = {π 1 , . . . , πn} be a (k, k − t)-SCID. Define S := π 1 , . . . , πn and I := π i ∩ π j | 1 ≤ i < j ≤ n . We establish several upper bounds for dim S + dim I in different situations. We give a spectrum result under certain conditions for n, giving examples of (k, k − t)-SCIDs reaching a large interval of values for dim S
more » ... f values for dim S + dim I.
doi:10.3934/amc.2020052 fatcat:wjq4lpgjcvfuxgnchzijmqhpuu