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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:On the number of discrete chains in the plane - N
óra Frankl (LSE)
DTSTART:20191107T140000Z
DTEND:20191107T150000Z
UID:TALK3901AT
URL:/talk/index/3901
DESCRIPTION:Determining the maximum number of unit distances t
hat can be spanned by n points in the plane is a d
ifficult problem\, which is wide open. The followi
ng more general question was recently considered b
y Eyvindur Ari Palsson\, Steven Senger\, and Adam
Sheffer. For given distances t_1\,...\,t_k a (k+1)
-tuple (p_1\,...\,p_{k+1}) is called a k-chain if
||x_i-x_{i+1}||=t_i for i=1\,...\,k. What is the m
aximum possible number of k-chains that can be spa
nned by a set of n points in the plane? Improving
the result of Palsson\, Senger and Sheffer\, we de
termine this maximum up to a polylogarithmic facto
r (which\, for k=1 mod 3 involves the maximum numb
er of unit distances). We also consider some gener
alisations\, and the analogous question in R^3. Jo
int work with Andrey Kupvaskii.
LOCATION:Watson LTB
CONTACT:Eoin Long
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