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CATEGORIES:Combinatorics Seminar
SUMMARY:Increasing Sequences of Integer Triples - Jason Lo
ng (University of Cambridge)
DTSTART;TZID=Europe/London:20161027T143000
DTEND;TZID=Europe/London:20161027T153000
UID:TALK68662AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68662
DESCRIPTION:We will consider the following deceptively simple
question\, formulated recently by Po Shen Loh who
connected it to an open problem in Ramsey Theory.
Define the '2-less than' relation on the set of tr
iples of integers by saying that a triple x is 2-l
ess than a triple y if x is less than y in at leas
t two coordinates. What is the maximal length of a
sequence of triples taking values in {1\,...\,n}
which is totally ordered by the '2-less than' rela
tion?\n\nIn his paper\, Loh uses the triangle remo
val lemma to improve on the trivial upper bound of
n^2^ by a factor of log*(n)\, and conjectures tha
t the truth should be of order n^(3/2). The gap be
tween these bounds has proved to be surprisingly r
esistant. We shall discuss joint work with Tim Gow
ers\, giving some developments towards this conjec
ture and a wide array of natural extensions of the
problem. Many of these extensions remain open.\n
LOCATION:MR12
CONTACT:Andrew Thomason
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