A Gessel-Viennot-Type Method for Cycle Systems in a Directed Graph
نویسنده
چکیده
We introduce a new determinantal method to count cycle systems in a directed graph that generalizes Gessel and Viennot’s determinantal method on path systems. The method gives new insight into the enumeration of domino tilings of Aztec diamonds, Aztec pillows, and related regions.
منابع مشابه
Ju n 20 00 From the Bethe Ansatz to the Gessel - Viennot Theorem
We state and prove several theorems that demonstrate how the coordinate Bethe Ansatz for the eigenvectors of suitable transfer matrices of a generalised inhomogeneous five-vertex model on the square lattice, given certain conditions hold, is equivalent to the Gessel-Viennot determinant for the number of configurations of N non-intersecting directed lattice paths, or vicious walkers, with variou...
متن کاملA Graph Theoretic Method for Determining Generating Sets of Prime Ideals in Oq(Mm,n(C))
We take a graph theoretic approach to the problem of finding generators for those prime ideals of Oq(Mm,n(C)) which are invariant under the torus action (C∗)m+n−1. Launois [12] has shown that the generators consist of certain quantum minors of the matrix of canonical generators of Oq(Mm,n(C)) and in [11] gives an algorithm to find them. In this paper we modify a classic result of Lindström [14]...
متن کاملEnumeration of octagonal random tilings by the Gessel-Viennot method
We propose the first algebraic determinantal formula to enumerate random rhombus tilings filling a centro-symmetric octagon of any size. This result uses the GesselViennot technique and generalizes to any octagon a former specialized formula by Elnitsky.
متن کاملLattice paths: vicious walkers and friendly walkers
In an earlier paper [4] the problem of vicious random walkers on a d-dimensional directed lattice was considered. \Vicious walkers" describes the situation in which two or more walkers arriving at the same lattice site annihilate one another. Accordingly, the only allowed con gurations are those in which contacts are forbidden. Alternatively expressed as a static rather than dynamic problem, vi...
متن کاملA combinatorial interpretation of the free-fermion condition of the six-vertex model
The free-fermion condition of the six-vertex model provides a five-parameter submanifold on which the Bethe ansatz equations for the wavenumbers that enter into the eigenfunctions of the transfer matrices of the model decouple, hence allowing explicit solutions. Such conditions arose originally in early field-theoretic S-matrix approaches. Here we provide a combinatorial explanation for the con...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 13 شماره
صفحات -
تاریخ انتشار 2006