Séminaire Lotharingien de Combinatoire, B76d (2018), 6 pp.

Laurent Demonet, Pierre-Guy Plamondon, Dylan Rupel, Salvatore Stella and Pavel Tumarkin

SL2-Tilings Do Not Exist in Higher Dimensions (mostly)

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.

Received: May 7, 2013. Revised: September 5, 2016. Accepted: March 31, 2017.

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