A Bijection Between Partially Directed Paths in the SymmetricWedge and Matchings
نویسندگان
چکیده
منابع مشابه
A Bijection Between Partially Directed Paths in the Symmetric Wedge and Matchings
We give a bijection between partially directed paths in the symmetric wedge y = ±x and matchings, which sends north steps to nestings. This gives a bijective proof of a result of Prellberg et al. that was first discovered through the corresponding generating functions: the number of partially directed paths starting at the origin confined to the symmetric wedge y = ±x with k north steps is equa...
متن کاملA Bijection between Well-labelled Positive Paths and Matchings
A well-labelled positive path of size n is a pair (p, σ) made of a word p = p1p2 . . . pn−1 on the alphabet {−1, 0,+1} such that ∑j i=1 pi ≥ 0 for all j = 1 . . . n−1, together with a permutation σ = σ1σ2 . . . σn of {1, . . . , n} such that pi = −1 implies σi < σi+1, while pi = 1 implies σi > σi+1. We establish a bijection between welllabelled positive paths of size n and matchings (i.e., fixe...
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The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetri...
متن کاملPartially directed paths in a symmetric wedge
The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and its solution. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to a symmetric wedge...
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We present a simple bijection between restricted Bressoud lattice paths and RSOS paths in regime II of the Andrews-Baxter-Forrester model. Both types of paths describe states in Z k parafermionic irreducible modules. The bijection implies a direct correspondence between a RSOS path and a parafermionic state in a quasi-particle basis.
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2011
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-011-0098-1