On minimal crossing number braid diagrams and homogeneous braids

Ilya Alekseev, Geidar Mamedov

Research output: Working paper


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.
Original languageEnglish
Number of pages14
StateE-pub ahead of print - 8 May 2019

Publication series

PublisherCornell University

Scopus subject areas

  • Algebra and Number Theory


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