Standard

On minimal crossing number braid diagrams and homogeneous braids. / Alekseev, Ilya; Mamedov, Geidar.

2019. (arXiv).

Research output: Working paper

Harvard

Alekseev, I & Mamedov, G 2019 'On minimal crossing number braid diagrams and homogeneous braids' arXiv. <https://arxiv.org/pdf/1905.03210.pdf>

APA

Alekseev, I., & Mamedov, G. (2019). On minimal crossing number braid diagrams and homogeneous braids. (arXiv). https://arxiv.org/pdf/1905.03210.pdf

Vancouver

Alekseev I, Mamedov G. On minimal crossing number braid diagrams and homogeneous braids. 2019 May 8. (arXiv).

Author

Alekseev, Ilya ; Mamedov, Geidar. / On minimal crossing number braid diagrams and homogeneous braids. 2019. (arXiv).

BibTeX

@techreport{a1336a51fdbb4d1f85bda5bd525c3669,
title = "On minimal crossing number braid diagrams and homogeneous braids",
abstract = "We study braid diagrams with a minimal number of crossings. Such braid diagrams correspond to geodesic words for the braid groups with standard Artin generators. We prove that a diagram of a homogeneous braid is minimal if and only if it is homogeneous. We conjecture that monoids of homogeneous braids are Artin-Tits monoids and prove that monoids of alternating braids are right-angled Artin monoids. Using this, we give a lower bound on the growth rate of the braid groups.",
author = "Ilya Alekseev and Geidar Mamedov",
year = "2019",
month = may,
day = "8",
language = "English",
series = "arXiv",
publisher = "Cornell University",
type = "WorkingPaper",
institution = "Cornell University",

}

RIS

TY - UNPB

T1 - On minimal crossing number braid diagrams and homogeneous braids

AU - Alekseev, Ilya

AU - Mamedov, Geidar

PY - 2019/5/8

Y1 - 2019/5/8

N2 - We study braid diagrams with a minimal number of crossings. Such braid diagrams correspond to geodesic words for the braid groups with standard Artin generators. We prove that a diagram of a homogeneous braid is minimal if and only if it is homogeneous. We conjecture that monoids of homogeneous braids are Artin-Tits monoids and prove that monoids of alternating braids are right-angled Artin monoids. Using this, we give a lower bound on the growth rate of the braid groups.

AB - We study braid diagrams with a minimal number of crossings. Such braid diagrams correspond to geodesic words for the braid groups with standard Artin generators. We prove that a diagram of a homogeneous braid is minimal if and only if it is homogeneous. We conjecture that monoids of homogeneous braids are Artin-Tits monoids and prove that monoids of alternating braids are right-angled Artin monoids. Using this, we give a lower bound on the growth rate of the braid groups.

UR - https://arxiv.org/abs/1905.03210

UR - https://www.semanticscholar.org/paper/On-minimal-crossing-number-braid-diagrams-and-Alekseev-Mamedov/ecbb80729f31a9986885fa35435cbf4e4ca7e406

M3 - Working paper

T3 - arXiv

BT - On minimal crossing number braid diagrams and homogeneous braids

ER -

ID: 75540466