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

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

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
• Public URL: https://durham-repository.worktribe.com/output/1384500
• Publisher URL: https://www.mat.univie.ac.at/~slc/wpapers/s76stella.html
• Related Public URLs: arxiv.org/abs/1604.02491