Standard

The language of geodesics for the discrete Heisenberg group. / Alekseev, Ilya; Magdiev, Ruslan.

в: arXiv, 08.05.2019.

Результаты исследований: Научные публикации в периодических изданиях › статья

Harvard

Alekseev, I & Magdiev, R 2019, 'The language of geodesics for the discrete Heisenberg group', arXiv. <https://arxiv.org/pdf/1905.03226.pdf>

APA

Alekseev, I., & Magdiev, R. (2019). The language of geodesics for the discrete Heisenberg group. arXiv, [03226]. https://arxiv.org/pdf/1905.03226.pdf

Vancouver

Alekseev I, Magdiev R. The language of geodesics for the discrete Heisenberg group. arXiv. 2019 Май 8. 03226.

Author

Alekseev, Ilya ; Magdiev, Ruslan. / The language of geodesics for the discrete Heisenberg group. в: arXiv. 2019.

BibTeX

@article{75a802a8f3ca4ad99ed8a3b0a033bf99,
title = "The language of geodesics for the discrete Heisenberg group",
abstract = "In this paper, we give a complete description of the language of geodesic words forthe discrete Heisenberg group H(Z) with respect to the standard two-element generating set. More precisely, we prove that the only dead end elements in H(Z) are nontrivial elements of the commutator subgroup. We give a description of their geodesic representatives, which are called dead end words. The description is based on a minimal perimeter polyomino concept. Finally, we prove that anygeodesic word in H(Z) is a prefix of a dead end word.",
author = "Ilya Alekseev and Ruslan Magdiev",
year = "2019",
month = may,
day = "8",
language = "English",
journal = "arXiv",
publisher = "Cornell University",

}

RIS

TY - JOUR

T1 - The language of geodesics for the discrete Heisenberg group

AU - Alekseev, Ilya

AU - Magdiev, Ruslan

PY - 2019/5/8

Y1 - 2019/5/8

N2 - In this paper, we give a complete description of the language of geodesic words forthe discrete Heisenberg group H(Z) with respect to the standard two-element generating set. More precisely, we prove that the only dead end elements in H(Z) are nontrivial elements of the commutator subgroup. We give a description of their geodesic representatives, which are called dead end words. The description is based on a minimal perimeter polyomino concept. Finally, we prove that anygeodesic word in H(Z) is a prefix of a dead end word.

AB - In this paper, we give a complete description of the language of geodesic words forthe discrete Heisenberg group H(Z) with respect to the standard two-element generating set. More precisely, we prove that the only dead end elements in H(Z) are nontrivial elements of the commutator subgroup. We give a description of their geodesic representatives, which are called dead end words. The description is based on a minimal perimeter polyomino concept. Finally, we prove that anygeodesic word in H(Z) is a prefix of a dead end word.

UR - https://arxiv.org/abs/1905.03226

M3 - Article

JO - arXiv

JF - arXiv

M1 - 03226

ER -

ID: 41478508