On the Number of Fully Packed Loop Configurations with a Fixed Associated Matching
نویسندگان
چکیده
منابع مشابه
On the Number of Fully Packed Loop Configurations with a Fixed Associated Matching
We show that the number of fully packed loop configurations corresponding to a matching with m nested arches is polynomial in m if m is large enough, thus essentially proving two conjectures by Zuber [Electronic J. Combin. 11(1) (2004), Article #R13].
متن کاملRefined 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. ...
متن کاملTriangular 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...
متن کاملSome 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...
متن کاملWieland 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...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2005
ISSN: 1077-8926
DOI: 10.37236/1873