$3$D Farey graph, lambda lengths and $SL_2$-tilings
Combinatorics
2023-06-30 v1
Abstract
We explore a three-dimensional counterpart of the Farey tessellation and its relations to Penner's lambda lengths and -tilings. In particular, we prove a three-dimensional version of Ptolemy relation, and generalise results of Ian Short to classify tame -tilings over Eisenstein integers in terms of pairs of paths in the 3D Farey graph.
Cite
@article{arxiv.2306.17118,
title = {$3$D Farey graph, lambda lengths and $SL_2$-tilings},
author = {Anna Felikson and Oleg Karpenkov and Khrystyna Serhiyenko and Pavel Tumarkin},
journal= {arXiv preprint arXiv:2306.17118},
year = {2023}
}
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32 pages