# P11516: Count permutations fixed at the level of RSK recording tableaux by reverse-complement

- ID: `P11516`
- Reference: `reverse-complement-permutations-with-equal-rsk-recording-tableau`
- Page: https://theoremdb.org/statements/P11516
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: b5a83bd9bdbf7dfdc7134c15b7360f889389e7bc
- Current Markdown: https://api.theoremdb.org/v1/statements/reverse-complement-permutations-with-equal-rsk-recording-tableau?representation=markdown
- Record maturity: Reviewed problem

## The problem

For (w\in \(S_n\)), let (w^{rc}) be the reverse-complement of its one-line notation and let (Q(w)) be its Robinson-Schensted recording tableau. Characterize the permutations satisfying (Q(w^{rc})=Q(w)), and find a closed formula in (n) for their number.

## Status

The reviewed record remains open.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `reverse-complement-permutations-with-equal-rsk-recording-tableau`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.