From the 1 of 90 linked papers with an AI index.
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The proportion of permutations fixing a -set
Ben Green, Mehtaab Sawhney
Denote by the limit, as , of the probability that a random permutation on a set of size has an invariant set of size . We give an asymptotic for…
On the maxima of Littlewood polynomials on
Brayden Letwin, Mehtaab Sawhney
A Littlewood polynomial is a polynomial of the form \[ f_n(x)=\sum_{k=0}^n \varepsilon_k x^k \] with . Let be i.i.d. Rademach…
Short proofs in combinatorics, probability and number theory II
Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2
We give a quintet of proofs resulting from questions posed by Erdős. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums, $…
Short proofs in combinatorics and number theory
Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2
We give a triplet of short proofs, each of which answers a question raised by Erdős. The first concerns the small prime factors of , the second concerns whether an ad…
On infinite sets with no on a line
Moe Putterman, Mehtaab Sawhney, Gregory Valiant
We give a construction of an infinite set of points in such that any subset has a constant density subset with no three points collinear and…