Wieland gyration for triangular fully packed loop configurations

2014/06/06 by Sabine Beil, Beil, Sabine, Ilse Fischer +3
Computer Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1406.1657

14 pages, 13 figures

arxiv created 2014/06/06 · openalex publication_date 2014/06/06 · arxiv updated 2014/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Triangular fully packed loop configurations (TFPLs) emerged as auxiliary objects in the study of fully packed loop configurations on a square (FPLs) corresponding to link patterns with a large number of nested arches. Wieland gyration, on the other hand, was invented to show the rotational invariance of the numbers A_π of FPLs corresponding to a given link pattern π. The focus of this article is the definition and study of Wieland gyration on TFPLs. We show that the repeated application of this gyration eventually leads to a configuration that is left invariant. We also provide a characterization of such stable configurations. Finally we apply our gyration to the study of TFPL configurations, in particular giving new and simple proofs of several results.

Citations

• Fully Packed Loops in a triangle: matchings, paths and puzzles

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