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CATEGORIES:Cambridge Philosophical Society
SUMMARY:The combinatorics of spaghetti hoops - Professor S
imon Tavaré FRS FMedSci\, Department of Applied M
athematics and Theoretical Physics and Cancer Res
earch UK Cambridge Institute
DTSTART;TZID=Europe/London:20181119T180000
DTEND;TZID=Europe/London:20181119T190000
UID:TALK109843AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/109843
DESCRIPTION:Starting with n cooked spaghetti strands\, tie ran
domly chosen ends together to produce a collection
of spaghetti hoops. What is the expected number o
f hoops? What can be said about the distribution o
f the number of hoops of length 1\, 2\, …? What is
the behaviour of the longest hoops when n is larg
e? What is the probability that all the hoops have
different lengths? Questions like this appear in
many guises in many areas of mathematics\, the con
nection being their relation to the Ewens Sampling
Formula (ESF). I will describe a number of relate
d examples\, including prime factorisation\, rando
m mappings and random permutations\, illustrating
the central role played by the ESF. I will also di
scuss methods for simulating decomposable combinat
orial structures by exploiting another wonder of t
he ESF world\, namely the Feller Coupling. Analysi
s of a children’s playground game shows that appar
ently small departures from the Feller model can o
pen up a number of unsolved problems.
LOCATION:Bristol-Myers Squibb Lecture Theatre\, Department
of Chemistry
CONTACT:Beverley Larner
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