Abstract

In this paper, we give a complete description of the language of geodesic words for
the 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 any
geodesic word in H(Z) is a prefix of a dead end word.
Original languageEnglish
Article number03226
Number of pages9
JournalarXiv
Publication statusE-pub ahead of print - 8 May 2019

Scopus subject areas

  • Algebra and Number Theory

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