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math.GR2019★ 1 cited
The language of geodesics for the discrete Heisenberg group
Ilya Alekseev, Ruslan Magdiev
In this paper, we give a complete description of the language of geodesic words for the discrete Heisenberg group with respect to the standard two-element generatin…
math.GR2019
On minimal crossing number braid diagrams and homogeneous braids
Ilya Alekseev, Geidar Mamedov
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 di…