Sufficiency of the necessary conditions for strippable IH_4(n;3)

Establish whether the necessary condition n congruent to 0 or 2 modulo 4 is sufficient for the existence of a strippable integer relative Heffter array IH_4(n;3), apart from the known nonexistence at n=4.

Background

For t=4 and k=3, the paper derives from its necessary-condition corollary that an IH_4(n;3) can exist only when n is congruent to 0 or 2 modulo 4. It proves that no strippable IH_4(4;3) exists, while computational evidence gives strippable examples for small even n greater than 4. The unresolved issue is whether the congruence condition is sufficient for every even n other than 4.

References

Computations show that a strippable $IH_4(n;3)$ does exist for small even $n>4$ but it is yet unknown if the necessary conditions are sufficient for all even $n\not=4$.

— Further constructions of square integer relative Heffter arrays  (2509.09907 - Donovan et al., 12 Sep 2025) in Section 2, “Strippable square integer relative Heffter arrays for k=3”