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Min-plus Bruhat decomposition — arXiv:2611.03896

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03896
License (as archived): CC0-1.0
Archived: 2026-11-04T12:48:58.477Z
SHA-256 of the archived text: 7ffca25546d64f1a179a1bf7dd2cb377f32a5d078a632dc8e6d6338fe1763738
Stable URL of this page: https://metraipolis.com/documento/dc_ea8fb6be95ca

How to cite

Min-plus Bruhat decomposition — arXiv:2611.03896 — arXiv (en), https://arxiv.org/abs/2611.03896 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ea8fb6be95ca (Metraipolis archive dc_ea8fb6be95ca, sha256 7ffca25546d64f1a179a1bf7dd2cb377f32a5d078a632dc8e6d6338fe1763738)

BibTeX

@misc{dcea8fb6be95ca,
  title = {Min-plus Bruhat decomposition — arXiv:2611.03896},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03896},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ea8fb6be95ca; sha256 7ffca25546d64f1a179a1bf7dd2cb377f32a5d078a632dc8e6d6338fe1763738},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03896. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study min-plus Bruhat cells $B_{trop}^{(n)} \odot p\odot B_{trop}^{(n)}$, where $B_{trop}^{(n)}$ denotes the set of all upper-triangular matrices over $\RR \cup \{\infty\}$, and $p$ is a permutation. It is proved that $\dim (B_{trop}^{(n)} \odot p \odot B_{trop}^{(n)})= \frac{n(n+1)}{2} + l(p)$, where $l(p)$ is the length of $p$ in Coxeter generators. Also we provide an explicit description of the cell $B_{trop}^{(n)}(\RR) \odot p_0\odot B_{trop}^{(n)}(\RR)$ (up to a subset of dimension less than $n^2$) for the highest in Bruhat order permutation $p_0$. Finally, it is shown that for a tropically non-singular matrix $A$ for at most one permutation $p_A$ it can hold $A\in B_{trop}^{(n)}\odot p_A\odot B_{trop}^{(n)}$.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Algebraic Geometry (math.AG) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.03896 — 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 2026-11-04T12:32:32.049Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).