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Durham University

Department of Mathematical Sciences


Publication details for Pavel Tumarkin

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

Author(s) from Durham


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.