English

SL_2-tilings and triangulations of the strip

Combinatorics 2018-12-14 v1 Representation Theory

Abstract

SL_2-tilings were introduced by Assem, Reutenauer, and Smith in connection with frieses and their applications to cluster algebras. An SL_2-tiling is a bi-infinite matrix of positive integers such that each adjacent 2 x 2-submatrix has determinant 1. We construct a large class of new SL_2-tilings which contains the previously known ones. More precisely, we show that there is a bijection between our class of SL_2-tilings and certain combinatorial objects, namely triangulations of the strip.

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Cite

@article{arxiv.1301.2456,
  title  = {SL_2-tilings and triangulations of the strip},
  author = {Thorsten Holm and Peter Jorgensen},
  journal= {arXiv preprint arXiv:1301.2456},
  year   = {2018}
}

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25 pages