Dennin’s Conjecture 8.9 on dual RSK correspondence

For every binary matrix $A$ , let $A^\dagger$ be its transpose-complement, and let $\operatorname{ins}(A)$ and $\operatorname{rec}(A)$ denote the insertion and recording tableaux in Dennin's variant of the dual RSK correspondence. The conjecture asserts the symmetry identity $\operatorname{ins}(A^\dagger)=\overline{\operatorname{rec}(A)}$ , where $\overline{\operatorname{rec}(A)}$ is the natural complement of the recording tableau. Equivalently, the dual RSK correspondence is symmetric on the relevant class of biGrassmannian permutations.

References

Primary source

arXiv

Additional references

Pipe Dream Rectification and Dual RSK Correspondence — arXiv

algebraic-combinatorics representation-theory

Posted 1 month ago

Progress summary

Refreshed 1 month ago

Claimed solved

A new preprint claims to settle Dennin’s conjecture about a symmetry in the dual RSK tableau correspondence, but the result has not been independently verified.

Dennin’s Conjecture $8.9$ asserts a structural symmetry for the dual RSK correspondence. The reported solution uses super-pipe-dream rectification to prove the symmetry and an associated identity.

Known results

Dennin (June 26, 2025) proved a related pipe-dream rectification bijection and derived a variant of dual RSK, but explicitly left Conjecture $8.9$ as conjectural.

August 2026 claimed proof

A report dated August 24, 2026 says the preprint Pipe Dream Rectification and Dual RSK Correspondence proves the conjectured symmetry and associated identity via super-pipe-dream rectification. This is an unrefereed arXiv solution claim; no independent verification was found in the retrieved material.

Current status (as of August 2026): A preprint claims that Conjecture $8.9$ is proved, but the claim remains unverified and no independent referee confirmation is recorded.

Sources

No solutions have been posted yet.