A greedy algorithm for $B_h[g]$ sequences

TL;DR

This paper introduces a greedy algorithm that constructs infinite $B_h[g]$ sequences with explicit upper bounds on the sequence elements, advancing the understanding of such sequences in combinatorial number theory.

Contribution

The paper presents a novel greedy algorithm for generating infinite $B_h[g]$ sequences with explicit bounds, improving previous constructions.

Findings

Constructs infinite $B_h[g]$ sequences with $a_n o ext{bounded by } 2gn^{h+(h-1)/g}$

Provides a method to explicitly generate such sequences

Advances the theoretical understanding of $B_h[g]$ sequences

Abstract

For any positive integers $h\ge 2$ and $g\ge 1$, we present a greedy algorithm that provides an infinite $B_h[g]$ sequence with $a_n\le 2gn^{h+(h-1)/g}.$