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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Solving linear equations in additive sets - Pablo
Candela (University of Cambridge)
DTSTART;TZID=Europe/London:20101123T160000
DTEND;TZID=Europe/London:20101123T170000
UID:TALK26182AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/26182
DESCRIPTION:Given an affine-linear form L in t variables with
integer coefficients\, a subset A of [N]={1\,2\,..
.\,N} is said to be L-free if A^t does not contain
any (non-trivial) solution of the equation L(x)=0
. The greatest cardinality that an L-free subset o
f [N] can have is denoted r_L(N).\n\nI will discus
s recent joint work with Olof Sisask which proves
the convergence of r_L(N)/N (and of other related
quantities) as N tends to infinity\, for any given
form L in at least 3 variables. The proof uses th
e discrete Fourier transform and tools from arithm
etic combinatorics. The convergence result address
es a question of Imre Ruzsa and extends work of Er
nie Croot.\n\nIn the different context where inter
vals [N] are replaced by cyclic groups of prime or
der\, we have similar convergence results\, and I
will discuss how in this context the limits can be
related to natural analogous quantities defined o
n the circle group.
LOCATION:MR4\, CMS
CONTACT:Tom Sanders
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