Details
| Original language | English |
|---|---|
| Pages (from-to) | 1817-1834 |
| Number of pages | 18 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 120 |
| Issue number | 7 |
| Publication status | Published - Sept 2013 |
Abstract
SL2-tilings were introduced by Assem, Reutenauer, and Smith in connection with frieses and their applications to cluster algebras. An SL2-tiling is a bi-infinite matrix of positive integers such that each adjacent 2 × 2-submatrix has determinant 1.In this paper we define the class of SL2-tilings with enough ones. It contains the previously known tilings as well as some which are new, and we show that it is in bijection with a certain class of combinatorial objects, namely "good" triangulations of the strip.
Keywords
- Arc, Conway-Coxeter friese, Ptolemy formula, Tiling, Triangulation
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Computer Science(all)
- Computational Theory and Mathematics
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In: Journal of Combinatorial Theory. Series A, Vol. 120, No. 7, 09.2013, p. 1817-1834.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - SL2-tilings and triangulations of the strip
AU - Holm, Thorsten
AU - Jørgensen, Peter
N1 - Funding Information: Part of this work was carried out while Peter Jørgensen was visiting Hannover. He thanks Thorsten Holm and the Institut für Algebra, Zahlentheorie und Diskrete Mathematik at the Leibniz Universität for their hospitality. He also gratefully acknowledges financial support from Thorsten Holmʼs grant HO 1880/5-1 , which is part of the research priority programme SPP 1388 Darstellungstheorie of the Deutsche Forschungsgemeinschaft (DFG).
PY - 2013/9
Y1 - 2013/9
N2 - SL2-tilings were introduced by Assem, Reutenauer, and Smith in connection with frieses and their applications to cluster algebras. An SL2-tiling is a bi-infinite matrix of positive integers such that each adjacent 2 × 2-submatrix has determinant 1.In this paper we define the class of SL2-tilings with enough ones. It contains the previously known tilings as well as some which are new, and we show that it is in bijection with a certain class of combinatorial objects, namely "good" triangulations of the strip.
AB - SL2-tilings were introduced by Assem, Reutenauer, and Smith in connection with frieses and their applications to cluster algebras. An SL2-tiling is a bi-infinite matrix of positive integers such that each adjacent 2 × 2-submatrix has determinant 1.In this paper we define the class of SL2-tilings with enough ones. It contains the previously known tilings as well as some which are new, and we show that it is in bijection with a certain class of combinatorial objects, namely "good" triangulations of the strip.
KW - Arc
KW - Conway-Coxeter friese
KW - Ptolemy formula
KW - Tiling
KW - Triangulation
UR - http://www.scopus.com/inward/record.url?scp=84880657805&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2013.07.001
DO - 10.1016/j.jcta.2013.07.001
M3 - Article
AN - SCOPUS:84880657805
VL - 120
SP - 1817
EP - 1834
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
SN - 0097-3165
IS - 7
ER -