Combinatorics of hexagonal fully packed loop configurations

Some combinatorics of rhomboid-shaped fully packed loop configurations

The study of rhomboid-shaped fully packed loop configurations (RFPLs) is inspired by the work of Fischer and Nadeau on triangular fully packed loop configurations (TFPLs). By using the same techniques as they did some nice combinatorics for RFPLs arise. To each RFPL and to each oriented RFPL a quadruple of binary words (α, β; γ, δ) – its so-called boundary – is assigned. There are necessary con...

Refined Counting of Fully Packed Loop Configurations

Abstract. We give a generalisation of a conjecture by Propp on a summation formula for fully packed loop configurations. The original conjecture states that the number of configurations in which each external edge is connected to its neighbour is equal to the total number of configurations of size one less. This conjecture was later generalised by Zuber to include more types of configurations. ...

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 (u, v;w) of 01-words encoding its boundary conditions that must necessarily satisfy d(u) + d(v) 6 d(w), where d(u) denotes the number of inversions in u. Wieland gyratio...

Wieland Drift for Triangular Fully Packed Loop Configurations

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 Aπ of FPLs corresponding to a given link pattern π. The focus of this article is...

Proof of two conjectures of Zuber on fully packed loop configurations