Maximum density of t-sumfree sequences

Determine whether the maximal density of any t-sumfree sequence is 1/t.

Background

The paper studies greedy strict t-sumfree sequences, whose entries avoid sums of t distinct previous values. Beyond periodicity, the authors mention a density question analogous to density problems for sumfree sets.

The proposed value 1/t is supported by results proved in the paper for certain 2-sumfree families, but the statement is presented only as a conjecture for arbitrary t-sumfree sequences.

References

For our sequences we only mention that it seems reasonable to conjecture that the maximal density for any $t$-sumfree sequence is $\frac{1}{t}$, compare Theorem \ref{thm:k2odd} and Theorem \ref{thm:2subs}.

— On $t$-sumfree sequences  (2609.16843 - Berkel et al., 15 Sep 2026) in Section 2, paragraph on sumfree sets and sequences