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Forbidden vector-valued intersections

Abstract:

We solve a generalised form of a conjecture of Kalai motivated by attempts to improve the bounds for Borsuk's problem. The conjecture can be roughly understood as asking for an analogue of the Frankl-R\"odl forbidden intersection theorem in which set intersections are vector-valued. We discover that the vector world is richer in surprising ways: in particular, Kalai's conjecture is false, but we prove a corrected statement that is essentially best possible, and applies to a considerably more ...

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Publication status:
Submitted
Peer review status:
Under review

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Mansfield College
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
Journal:
arXiv
Publication date:
2018-01-01
Pubs id:
pubs:701182
URN:
uri:316c4277-8322-4f27-8f1f-ebf1089a7cf2
UUID:
uuid:316c4277-8322-4f27-8f1f-ebf1089a7cf2
Local pid:
pubs:701182
Keywords:

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