Ternary-digit characterization of extra edge-connectivity minimizers

Characterize directly by the ternary digits all sizes h for which the extra edge connectivity λ_h(Q_n^3) equals the boundary count ξ_n(h), for the ternary Hamming cube Q_n^3.

Background

For the ternary Hamming cube Q_n3, the paper relates the extra edge connectivity λ_h(Q_n3) to the minimum of the boundary counts ξ_n(m) over h≤m≤3n−h. Several families of sizes h for which λ_h(Q_n3)=ξ_n(h) are known, including ranges established in prior work, but a direct characterization in terms of ternary digits remains unresolved.

References

Can all such sizes $h$ be described directly by their ternary digits?

— Local Extrema and Infinite Derivatives of the Delange Function of Base 3  (2610.21265 - Zhu, 15 Oct 2026) in Section “Other bases and further questions”