On wild frieze patterns. (English) Zbl 1367.05207
Summary: In this article, among other things, we show: (1) There are periodic wild \(\mathrm{SL}_3\)-frieze patterns whose entries are positive integers. (2) There are non-periodic \(\mathrm{SL}_3\)-frieze patterns whose entries are positive integers. (3) There is an \(\mathrm{SL}_3\)-frieze pattern whose entries are positive integers and with infinitely many different entries.
MSC:
| 05E10 | Combinatorial aspects of representation theory |
| 05B05 | Combinatorial aspects of block designs |
| 13F60 | Cluster algebras |
References:
| [1] | Bergeron [Bergeron and Reutenauer 10] F., Illinois J. Math. 54 (1) pp 263– (2010) |
| [2] | DOI: 10.4171/CMH/65 · Zbl 1119.16013 · doi:10.4171/CMH/65 |
| [3] | DOI: 10.2307/3615344 · Zbl 0285.05028 · doi:10.2307/3615344 |
| [4] | DOI: 10.1215/S0012-7094-72-03970-1 · doi:10.1215/S0012-7094-72-03970-1 |
| [5] | Coxeter [Coxeter 71] H. S. M., Acta Arith. 18 pp 297– (1971) |
| [6] | DOI: 10.1016/j.ejc.2014.06.005 · Zbl 1342.52025 · doi:10.1016/j.ejc.2014.06.005 |
| [7] | DOI: 10.2140/ant.2009.3.317 · Zbl 1181.20035 · doi:10.2140/ant.2009.3.317 |
| [8] | DOI: 10.1016/j.jcta.2010.12.003 · Zbl 1231.05305 · doi:10.1016/j.jcta.2010.12.003 |
| [9] | DOI: 10.1007/s10801-012-0348-2 · Zbl 1259.05191 · doi:10.1007/s10801-012-0348-2 |
| [10] | DOI: 10.1112/blms/bdv070 · Zbl 1330.05035 · doi:10.1112/blms/bdv070 |
| [11] | DOI: 10.1017/fms.2014.20 · Zbl 1297.39004 · doi:10.1017/fms.2014.20 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
