Corner Itineraries and Resonance of ASM Superpromotion
Manuscript 5 October 2026 · Online 5 October 2026
Abstract
We construct an explicit binary-word factor of Striker–Williams superpromotion on alternating sign matrices of order \(n\). The membership indicator of a specified corner of the ASM poset returns after \(3n-2\) steps. Its itinerary of that length therefore intertwines superpromotion with cyclic rotation.
For \(n\geq3\), rotation on the image has effective order exactly \(3n-2\); the \(n=2\) exception has effective order \(2\). The proof combines a face-stratum bijection with time-shift recombination on the tetrahedral poset and does not enumerate full orbits. Evaluation takes \(O(n^4)\) elementary toggle tests.
This is a dynamical itinerary factor, not a static noncrossing model or the proposed order-polytope projection.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Corner-factor theorem
- Categories
- math.CO
- Manuscript
- 5 October 2026
- Online release
- 5 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Corner Itineraries and Resonance of ASM Superpromotion,” EulerSolve Research Papers, AIM-OTHER-0011, 2026. https://doi.org/10.5281/zenodo.23160691.
BibTeX
@misc{Ferudun2026CornerResonance,
author = {Ferudun, Alper},
title = {Corner Itineraries and Resonance of ASM Superpromotion},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-other-0011/},
doi = {10.5281/zenodo.23160691},
note = {AIM-OTHER-0011; unrefereed preprint}
}