SL(2)-tilings do not exist in higher dimensions (mostly)

Demonet, L.; Plamondon, P.-G.; Rupel, D.; Stella, S.; Tumarkin, P.

SL(2)-tilings do not exist in higher dimensions (mostly)

Demonet, L.; Plamondon, P.-G.; Rupel, D.; Stella, S.; Tumarkin, P.

Authors

L. Demonet

P.-G. Plamondon

D. Rupel

S. Stella

Professor Pavel Tumarkin pavel.tumarkin@durham.ac.uk
Professor

Abstract

We define a family of generalizations of SL2-tilings to higher dimensions called ϵ-SL2-tilings. We show that, in each dimension 3 or greater, ϵ-SL2-tilings exist only for certain choices of ϵ. In the case that they exist, we show that they are essentially unique and have a concrete description in terms of odd Fibonacci numbers.

Citation

Demonet, L., Plamondon, P., Rupel, D., Stella, S., & Tumarkin, P. (2018). SL(2)-tilings do not exist in higher dimensions (mostly). Séminaire lotharingien de combinatoire, 76, Article B76d

Journal Article Type	Article
Acceptance Date	Mar 31, 2017
Online Publication Date	Sep 12, 2018
Publication Date	Sep 12, 2018
Deposit Date	Apr 12, 2016
Publicly Available Date	Apr 5, 2017
Journal	Séminaire lotharingien de combinatoire
Publisher	Fakultät für Mathematik, Universität Wien
Peer Reviewed	Peer Reviewed
Volume	76
Article Number	B76d
Publisher URL	https://www.mat.univie.ac.at/~slc/wpapers/s76stella.html
Related Public URLs	arxiv.org/abs/1604.02491