Classification of heavy partitions

Characterize all partitions that are heavy under PNim.

Background

The paper establishes heaviness for several structured families of partitions and gives computational data for all heavy partitions of order at most 8, up to conjugation. However, it does not provide a general characterization, instead explicitly asking which partitions are heavy.

References

Which partitions are heavy?

— Nim on Integer Partitions and Hyperrectangles  (2506.04991 - Gottlieb et al., 5 Jun 2025) in Question 2 (conj:heavy), Section 5, Conclusion