## Publicacions Matemàtiques

### Dense Infinite $B_h$ Sequences

#### Abstract

For $h=3$ and $h=4$ we prove the existence of infinite $B_h$ sequences $\mathcal{B}$ with counting function

$$\mathcal{B}(x)= x^{\sqrt{(h-1)^2+1}-(h-1) + o(1)}.$$

This result extends a construction of I. Ruzsa for $B_2$ sequences.

#### Article information

Source
Publ. Mat., Volume 59, Number 1 (2015), 55-73.

Dates
First available in Project Euclid: 21 January 2015

https://projecteuclid.org/euclid.pm/1421861993

Mathematical Reviews number (MathSciNet)
MR3302576

Zentralblatt MATH identifier
1307.45008

Subjects
Primary: 11B83: Special sequences and polynomials

#### Citation

Cilleruelo, Javier; Tesoro, Rafael. Dense Infinite $B_h$ Sequences. Publ. Mat. 59 (2015), no. 1, 55--73. https://projecteuclid.org/euclid.pm/1421861993