Geodesic
Triangular fully packed loop configurations of excess 2
Sabine Beil1
1University of Vienna
The electronic journal of combinatorics, Tome 23 (2016) no. 4
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Triangular fully packed loop configurations (TFPLs) came up in the study of fully packed loop configurations on a square (FPLs) corresponding to link patterns with a large number of nested arches. To a TFPL is assigned a triple $(u,v;w)$ of $01$-words encoding its boundary conditions which must necessarily satisfy that $d(u)+d(v)\leq d(w)$, where $d(u)$ denotes the number of inversions in $u$. Wieland gyration, on the other hand, was invented to show the rotational invariance of the numbers of FPLs having given link patterns. Later, Wieland drift — a map on TFPLs that is based on Wieland gyration — was defined. The main contribution of this article will be a linear expression for the number of TFPLs with boundary $(u,v;w)$ where $d(w)-d(u)-d(v)=2$ in terms of numbers of stable TFPLs, that is, TFPLs invariant under Wieland drift. This linear expression generalises already existing enumeration results for TFPLs with boundary $(u,v;w)$ where $d(w)-d(u)-d(v)=0,1$.
DOI : 10.37236/5536
Classification : 05A15, 05A19
Mots-clés : triangular fully packed loop configurations, Wieland gyration

Sabine Beil  1

1 University of Vienna 
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Sabine Beil. Triangular fully packed loop configurations of excess 2. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/5536

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