# P11730: Does Kimberling's expulsion diagonal contain every positive integer?

- ID: `P11730`
- Reference: `does-kimberling-s-expulsion-diagonal-contain-every-positive-integer`
- Page: https://theoremdb.org/statements/P11730
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: 8761a3148f04464c77e33962395dfa4a75cd2b51
- Current Markdown: https://api.theoremdb.org/v1/statements/does-kimberling-s-expulsion-diagonal-contain-every-positive-integer?representation=markdown
- Record maturity: Reviewed problem

## The problem

Start with row \(1\) equal to \(1,2,3,\ldots\). To make row \(r+1\) from row \(r\), list the entry immediately right of row \(r\)'s diagonal entry, then the first entry left of it, then the second right, second left, and so on, continuing with new consecutive integers when the finite left side is exhausted. Prove that the main diagonal of the resulting array is a permutation of the positive integers.

## 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 `does-kimberling-s-expulsion-diagonal-contain-every-positive-integer`, 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.