G. Shakan

activity

20052020

most citedOn distinct consecutive differences

1 citations · 1 across the 3 of their papers we have counts for

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5 papers · 1 filter

math.CO2019

On distinct consecutive differences

Imre Ruzsa, George Shakan, Jozsef Solymosi +1

We show that if $A = {a_{1} < a_{2} < \dots < a_{k}}$ is a set of real numbers such that the differences of the consecutive elements are distinct, then for and finite $B \subset \mathbb…

math.CO2018

Stronger sum-product inequalities for small sets

Misha Rudnev, George Shakan, Ilya Shkredov

Let $F$ be a field and a finite $A \subset F$ be sufficiently small in terms of the characteristic $p$ of $F$ if $p > 0$ . We strengthen the "threshold" sum-product inequality $$|AA|^3…

math.CO2018

Breaking the 6/5 threshold for sums and products modulo a prime

G. Shakan, I. D. Shkredov

Let $A \subset F_{p}$ of size at most $p^{3/5}$ . We show $∣ A + A ∣ + ∣ AA ∣ ≳ ∣ A ∣^{6/5 + c},$ for $c = 4/305$ . Our main tools are the cartesian product point--line incide…

math.CO2018

Monochromatic Hilbert cubes and arithmetic progressions

József Balogh, Mikhail Lavrov, George Shakan +1

The Van der Waerden number $W (k, r)$ denotes the smallest $n$ such that whenever $[n]$ is $r$ --colored there exists a monochromatic arithmetic progression of length $k$ . Similarly,…

math.CO2005★ 1 cited

On distinct consecutive differences

J. Solymosi

We show that if $A = {a_{1}, a_{2}, ..., a_{k}}$ is a monotone increasing set of numbers, and the differences of the consecutive elements are all distinct, then $∣ A + B ∣ \geq c ∣ A ∣^{1/2} ∣ B ∣$ f…