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University of Cambridge > Talks.cam > Discrete Analysis Seminar > Solving linear equations in additive sets

## Solving linear equations in additive setsAdd to your list(s) Download to your calendar using vCal - Pablo Candela (University of Cambridge)
- Tuesday 23 November 2010, 16:00-17:00
- MR4, CMS.
If you have a question about this talk, please contact Tom Sanders. 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 of [N] can have is denoted r_L(N). I will discuss 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 the discrete Fourier transform and tools from arithmetic combinatorics. The convergence result addresses a question of Imre Ruzsa and extends work of Ernie Croot. In the different context where intervals [N] are replaced by cyclic groups of prime order, we have similar convergence results, and I will discuss how in this context the limits can be related to natural analogous quantities defined on the circle group. This talk is part of the Discrete Analysis Seminar series. ## This talk is included in these lists:- All CMS events
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