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.
@article{10_37236_4438,
author = {Sabine Beil and Ilse Fischer and Philippe Nadeau},
title = {Wieland drift for triangular fully packed loop configurations},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4438},
zbl = {1307.05008},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4438/}
}
TY - JOUR
AU - Sabine Beil
AU - Ilse Fischer
AU - Philippe Nadeau
TI - Wieland drift for triangular fully packed loop configurations
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/4438/
DO - 10.37236/4438
ID - 10_37236_4438
ER -
%0 Journal Article
%A Sabine Beil
%A Ilse Fischer
%A Philippe Nadeau
%T Wieland drift for triangular fully packed loop configurations
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4438/
%R 10.37236/4438
%F 10_37236_4438
Sabine Beil; Ilse Fischer; Philippe Nadeau. Wieland drift for triangular fully packed loop configurations. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4438
