An explicit finite $B_k$-sequence

TL;DR

This paper presents a method to explicitly construct finite $B_k$-sequences with polynomial-time computability, providing sequences of size $n$ with elements bounded by $n^{k+o(k)}$, advancing combinatorial sequence construction.

Contribution

It offers the first explicit, polynomial-time constructible $B_k$-sequence of size $n$ with bounded elements, improving previous non-constructive existence results.

Findings

Explicit construction of $B_k$-sequences in polynomial time

Sequences of size $n$ with elements bounded by $n^{k+o(k)}$

Advancement in combinatorial sequence theory

Abstract

For any $n$ and $k$, we provide an explicit (that is, computable in polynomial time) example of integer $B_k$-sequence of size $n$ consisting of elements bounded by $n^{k+o(k)}$.