scholarly journals Product sets cannot contain long arithmetic progressions

2013 ◽  
Vol 43 ◽  
pp. 169-170
Author(s):  
Dmitry Zhelezov
Keyword(s):  
Arithmetic Progressions ◽  
Product Sets

scholarly journals Product sets cannot contain long arithmetic progressions

2014 ◽  
Vol 163 (4) ◽  
pp. 299-307 ◽  
Author(s):  
Dmitrii Zhelezov
Keyword(s):  
Arithmetic Progressions ◽  
Product Sets

scholarly journals Improved bounds for arithmetic progressions in product sets

2015 ◽  
Vol 11 (08) ◽  
pp. 2295-2303 ◽  
Author(s):  
Dmitrii Zhelezov
Keyword(s):  
Lower Bound ◽  
Arithmetic Progression ◽  
Arithmetic Progressions ◽  
Complex Numbers ◽  
Natural Numbers ◽  
Multiplicative Constant ◽  
Product Sets

Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic progression contained in the product set B.B = {bb′|b, b′ ∈ B} cannot be greater than O(n log n) which matches the lower bound provided in an earlier paper up to a multiplicative constant. For sets of complex numbers, we improve the bound to Oϵ(n1 + ϵ) for arbitrary ϵ > 0 assuming the GRH.

scholarly journals Colorings with only rainbow arithmetic progressions

2020 ◽  
Vol 161 (2) ◽  
pp. 507-515
Author(s):  
J. Pach ◽  
I. Tomon
Keyword(s):  
Arithmetic Progressions
Sign in / Sign up

Export Citation Format

Share Document