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Genlex Gray codes for $S_n$ with the fewest operations: classification and symmetry — arXiv:2609.13214

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.13214
License (as archived): CC0-1.0
Archived: 2026-10-16T01:22:58.259Z
SHA-256 of the archived text: 68c3d1fead591762a0b7643eec5c7ca235adc47f1cfa9db9bc1886e9edc72f8d
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How to cite

Genlex Gray codes for $S_n$ with the fewest operations: classification and symmetry — arXiv:2609.13214 — arXiv (en), https://arxiv.org/abs/2609.13214 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_02a79eb3ca95 (Metraipolis archive dc_02a79eb3ca95, sha256 68c3d1fead591762a0b7643eec5c7ca235adc47f1cfa9db9bc1886e9edc72f8d)

BibTeX

@misc{dc02a79eb3ca95,
  title = {Genlex Gray codes for $S_n$ with the fewest operations: classification and symmetry — arXiv:2609.13214},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.13214},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_02a79eb3ca95; sha256 68c3d1fead591762a0b7643eec5c7ca235adc47f1cfa9db9bc1886e9edc72f8d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.13214. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A Gray code for $S_n$ is \emph{genlex} when words sharing a suffix are consecutive. We determine the genlex Gray codes for $S_n$ that use the fewest possible operations: Zaks' recursion generalises to a superfactorial family of such codes, and no code outside this family attains the minimum. Every code in the family closes into a cycle, and the cycle is invariant under a group of left translations, cyclic of order $n$ or dihedral of order $2n$ according to an explicit criterion on the operations. In the pancake graph the family reduces to a single member, the classical Zaks order; with respect to the standard parabolic chain of $W(A_{n-1})$, that order attains one extreme of total Coxeter length.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-15 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.13214 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T00:39:30.162Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).