Séminaire Lotharingien de Combinatoire, B76e (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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