Wieland Drift for Triangular Fully Packed Loop Configurations

Sabine Beil, Ilse Fischer, Philippe Nadeau

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 $A_\pi$ of FPLs corresponding to a given link pattern $\pi$. The focus of this article is the definition and study of Wieland drift on TFPLs. We show that the repeated application of this operation eventually leads to a configuration that is left invariant. We also provide a characterization of such stable configurations. Finally we apply Wieland drift to the study of TFPL configurations, in particular giving new and simple proofs of several results.

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