• 1 Fakultät für Mathematik [Wien]

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. A necessary condition for the boundary $(u,v;w)$ of a TFPL is $\lvert \lambda(u) \rvert +\lvert \lambda(v) \rvert \leq \lvert \lambda(w) \rvert$, where $\lambda(u)$ denotes the Young diagram associated with the $01$-word $u$. 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 $\pi$. Later, Wieland drift was defined as the natural adaption of Wieland gyration to TFPLs. The main contribution of this article is a linear expression for the number of TFPLs with boundary $(u,v;w)$ where $\lvert \lambda (w) \rvert - \lvert\lambda (u) \rvert - \lvert \lambda (v)\rvert \leq 2$ in terms of numbers of stable TFPLs that is TFPLs invariant under Wieland drift. These stable TFPLs have boundary $(u^{+},v^{+};w)$ for words $u^{+}$ and $v^{+}$ such that $\lambda (u) \subseteq \lambda (u^{+})$ and $\lambda (v) \subseteq \lambda (v^{+})$.