Metraipolis › archive › dc_e447daa797db

Avoiding patterns with three distinct letters in Canon permutations — arXiv:2608.30002

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.30002
License (as archived): CC0-1.0
Archived: 2026-10-17T09:31:07.239Z
SHA-256 of the archived text: df9ff87673701784474c24e6b303548b39df3d1796256b67a337a8e9f73ae2c5
Stable URL of this page: https://metraipolis.com/documento/dc_e447daa797db

How to cite

Avoiding patterns with three distinct letters in Canon permutations — arXiv:2608.30002 — arXiv (en), https://arxiv.org/abs/2608.30002 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e447daa797db (Metraipolis archive dc_e447daa797db, sha256 df9ff87673701784474c24e6b303548b39df3d1796256b67a337a8e9f73ae2c5)

BibTeX

@misc{dce447daa797db,
  title = {Avoiding patterns with three distinct letters in Canon permutations — arXiv:2608.30002},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.30002},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e447daa797db; sha256 df9ff87673701784474c24e6b303548b39df3d1796256b67a337a8e9f73ae2c5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.30002. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study avoidance of patterns of length $3$ with three distinct letters in canon permutations. We reduce the problem to studying pattern avoidance in lattice words and show that there are $6$ such pattern avoiding classes. This shows that there are $12$ classes for the original Canon permutation pattern avoidance problem. We also give descent refinements for these classes and classify the patterns for which the descent enumeration gives palindromic and $\gamma$-positive polynomials. When the polynomials are $\gamma$-positive, we explain the $\gamma$-positivity through a group action analogous to Foata-Strehl valley hopping. Additionally, we study the avoidance of patterns in the relabelling orbit of $1213, 12112, 1231$ after a conjecture about their cardinalities by Laudone and give bijective proofs for the results.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.30002 — 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 2026-10-17T09:02:28.841Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).