Edge reconstruction for immanants associated with hook partitions

Determine whether, for every hook partition λ of n, the immanant function dλ satisfies the edge reconstruction conjecture.

Background

The second immanant is one particular immanant associated with an irreducible character of the symmetric group. After proving reconstruction results for second immanantal polynomials, the paper asks whether the same type of edge-reconstruction property extends to the immanant function associated with every hook partition λ of n. This broader question is explicitly identified as future work and remains unresolved in the paper.

References

  1. For each hook partition X of n, can the immanant function dy satisfy the edge reconstruc- tion conjecture?
— On the edge reconstruction of the second immanantal polynomials of undirected graph and digraph  (2502.12781 - Wu et al., 18 Feb 2025) in Section 4, Summary