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Length-generating functions for twisted involutions of Coxeter groups — arXiv:2609.08000

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.08000
License (as archived): CC0-1.0
Archived: 2026-10-16T14:49:25.428Z
SHA-256 of the archived text: 59bf84b64d81b19222a411f54becfca21641b2c7cd3ad5da3f53b7e1d12d615e
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How to cite

Length-generating functions for twisted involutions of Coxeter groups — arXiv:2609.08000 — arXiv (en), https://arxiv.org/abs/2609.08000 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_50ef13a136cf (Metraipolis archive dc_50ef13a136cf, sha256 59bf84b64d81b19222a411f54becfca21641b2c7cd3ad5da3f53b7e1d12d615e)

BibTeX

@misc{dc50ef13a136cf,
  title = {Length-generating functions for twisted involutions of Coxeter groups — arXiv:2609.08000},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.08000},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_50ef13a136cf; sha256 59bf84b64d81b19222a411f54becfca21641b2c7cd3ad5da3f53b7e1d12d615e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.08000. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For a Coxeter system $(W,S)$ of finite rank and an involutive automorphism $\ast:W\to W$ which preserves $S$, we prove that the length-generating function $\sum_{z\in\mathbf{I}_{W,\ast}}q^{\ell(z)}$ of the set of $\ast$-twisted involutions is rational. We derive recurrence relations analogous to the well-known recurrence relations expressing the growth series $W(q):=\sum_{w\in W}q^{\ell(w)}$ in terms of the growth series $W_I(q)$ of the parabolic subgroups of $W$. Our result extends to any subset $\mathcal{C}$ of $\ast$-twisted involutions that is closed under $\ast$-twisted conjugation. We use these recurrence relations to give an alternative proof of a power-series identity for twisted involutions due to Lusztig.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.CO).
Categorie arXiv: Group Theory (math.GR) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.08000 — 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 2026-10-16T14:32:29.940Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).