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SL_2-Tilings Do Not Exist in Higher Dimensions (mostly)

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journal contribution
posted on 20.05.2019, 14:16 by L Demonet, P-G Plamondon, D Rupel, S Stella, P Tumarkin
We define a family of generalizations of SL2-tilings to higher dimensions called epsilon-SL2-tilings. We show that, in each dimension 3 or greater, epsilon-SL2-tilings exist only for certain choices of epsilon. In the case that they exist, we show that they are essentially unique and have a concrete description in terms of odd Fibonacci numbers.

Funding

The first author was partially supported by JSPS Grant-in-Aid for Young Scientist (B) 26800008. The second author was partially supported by the French ANR grant SC3A (ANR-15-CE40-0004-01)

History

Citation

Séminaire Lotharingien de Combinatoire, 2018, 76, B76d.

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Séminaire Lotharingien de Combinatoire

Publisher

The Séminaire Lotharingien de Combinatoire, Copyright Dominique Foata, Guoniu Han, Alain Sartout and Christian Krattenthaler

issn

1286-4889

Acceptance date

31/03/2017

Copyright date

2018

Available date

20/05/2019

Publisher version

https://www.mat.univie.ac.at/~slc/wpapers/s76stella.html

Language

en