Link invariants, the chromatic polynomial and the Potts model
نویسندگان
چکیده
منابع مشابه
8 Link Invariants , the Chromatic Polynomial and the Potts Model
We study the connections between link invariants, the chromatic polynomial, geometric representations of models of statistical mechanics, and their common underlying algebraic structure. We establish a relation between several algebras and their associated combinatorial and topological quantities. In particular, we define the chromatic algebra, whose Markov trace is the chromatic polynomial χQ ...
متن کاملSe p 20 09 LINK INVARIANTS , THE CHROMATIC POLYNOMIAL AND THE POTTS MODEL
We study the connections between link invariants, the chromatic polynomial, geometric representations of models of statistical mechanics, and their common underlying algebraic structure. We establish a relation between several algebras and their associated combinatorial and topological quantities. In particular, we define the chromatic algebra, whose Markov trace is the chromatic polynomial χQ ...
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Abstract. The U -polynomial of Noble and Welsh is known to have intimate connections with the Potts model as well as with several important graph polynomials. For each graph G, U(G) is equivalent to Stanley’s symmetric bad colouring polynomial XB(G). Moreover Sarmiento established the equivalence between U and the polychromate of Brylawski. Loebl defined the q-dichromate Bq(G, x, y) as a functi...
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A new link invariant is derived using the exactly solvable chiral Potts model and a generalized Gaussian summation identity. Starting from a general formulation of link invariants using edge-interaction spin models, we establish the uniqueness of the invariant for self-dual models. We next apply the formulation to the self-dual chiral Potts model, and obtain a link invariant in the form of a la...
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Chromatic polynomials are important objects in graph theory and statistical physics, but as a result of computational difficulties, their study is limited to graphs that are small, highly structured, or very sparse. We have devised and implemented two algorithms that approximate the coefficients of the chromatic polynomial P (G,x), where P (G, k) is the number of proper k-colorings of a graph G...
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ژورنال
عنوان ژورنال: Advances in Theoretical and Mathematical Physics
سال: 2010
ISSN: 1095-0761,1095-0753
DOI: 10.4310/atmp.2010.v14.n2.a4