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

Demonet, L. and Plamondon, P.-G. and Rupel, D. and Stella, S. and Tumarkin, P. (2018) 'SL(2)-tilings do not exist in higher dimensions (mostly).', Séminaire Lotharingien de Combinatoire., 76 . B76d.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Date accepted:31 March 2017
Date deposited:05 April 2017
Date of first online publication:12 September 2018
Date first made open access:17 June 2021

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