# Mathematical Research at the University of Cambridge

What are the possible intersection sizes that a k-dimensional subspace can have with the vertices of the n-dimensional hypercube (in Euclidean space)? Melo and Winter [arXiv:1712.01763, 2017] conjectured that all intersection sizes larger than 2 to the {k-1} (the “large” sizes) are of the form 2 to the {k-1} + 2 to the i. We show that this is almost true: the large intersection sizes are either
of this form or of the form 35·2 to the {k-6} . We also disprove a second conjecture of Melo and Winter by proving that a positive fraction of the “small” values is missing.
Joint work with Tom Johnson

07Nov
Nov 7th 2019
14:30 to 15:30

MR12

## Speaker:

Carla Groenland (University of Oxford)