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                * Princeton Discrete Math Seminar *
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Speaker: Hans Yo (Princeton)

Thursday 5th October, 3:00 in Fine Hall 224.

Title: Tight bound and structural theorem for joints

The joints problem asks to determine the maximum number of joints N lines
can form, where a joint in a d-dimensional space is a point on d lines in
linearly independent directions. Recently, Ting-Wei Chao and I determined
the maximum exactly for k choose d-1 lines in d-dimensional space, namely k
choose d. What is more important is that we are able to prove a structural
result determining all optimal configurations, and this is the first success
of the polynomial method in this direction. It turns out that our result
implies a conjecture of Bollobás and Eccles as an immediate corollary
regarding a generalization of the Kruskal–Katona theorem. In this talk, I
will talk about the connection to that conjecture and also give a high-level
overview of the key ideas.

Based on joint work with Ting-Wei Chao


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