3 research outputs found
Triangular fully packed loop configurations of excess 2
International audienceTriangular 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 of -words encoding its boundary conditions. A necessary condition for the boundary of a TFPL is , where denotes the Young diagram associated with the -word . Wieland gyration, on the other hand, was invented to show the rotational invariance of the numbers of FPLs corresponding to a given link pattern . 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 where in terms of numbers of stable TFPLs that is TFPLs invariant under Wieland drift. These stable TFPLs have boundary for words and such that and .Les configurations de boucles compactes triangulaires (”triangular fully packed loop configurations”, ou TFPLs) sont apparues dans l’étude des configurations de boucles compactes dans un carré (FPLs) correspondant à des motifs de liaison avec un grand nombre d’arcs imbriqués. À chaque TPFL on associe un triplet de mots sur {0,1}, qui encode ses conditions aux bords. Une condition nécessaire pour le bord d’un TFPL est , où désigne le diagramme de Young associé au mot . D’un autre côté, la giration de Wieland a été inventée pour montrer l’invariance par rotation des nombres de FPLs correspondant à un motif de liaison donné . Plus tard, la déviation de Wieland a été définie pour adapter de manière naturelle la giration de Wieland aux TFPLs. La contribution principale de cet article est une expression linéaire pour le nombre de TFPLs de bord , où , en fonction des nombres de TFPLs stables, i.e., les TFPLs invariants par déviation de Wieland. Ces TFPLs stables ont pour bord , avec et des mots tels que et
Triangular fully packed loop configurations of excess 2
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 of -words encoding its boundary conditions. A necessary condition for the boundary of a TFPL is , where denotes the Young diagram associated with the -word . Wieland gyration, on the other hand, was invented to show the rotational invariance of the numbers of FPLs corresponding to a given link pattern . 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 where in terms of numbers of stable TFPLs that is TFPLs invariant under Wieland drift. These stable TFPLs have boundary for words and such that and
Wieland drift for triangular fully packed loop configurations
International audienceTriangular 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 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