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SUMMARY:Intersection sizes of linear subspaces with the hypercube -  Carla
  Groenland (University of Oxford)
DTSTART:20191107T143000Z
DTEND:20191107T153000Z
UID:TALK125686@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:What are the possible intersection sizes that a k-dimensional 
 subspace can have with the vertices of the n-dimensional hypercube (in Euc
 lidean 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 t
 rue: the large intersection sizes are either\nof this form or of the form 
 35·2 to the {k-6} . We also disprove a second conjecture of Melo and Wint
 er by proving that a positive fraction of the “small” values is missin
 g.\nJoint work with Tom Johnson
LOCATION:MR12
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