On partition functions for 3-graphs
نویسندگان
چکیده
Abstract. A cyclic graph is a graph with at each vertex a cyclic order of the edges incident with it specified. We characterize which real-valued functions on the collection of cubic cyclic graphs are partition functions of a real vertex model (P. de la Harpe, V.F.R. Jones, Graph invariants related to statistical mechanical models: examples and problems, Journal of Combinatorial Theory, Series B 57 (1993) 207–227). They are characterized by ‘weak reflection positivity’, which amounts to the positive semidefiniteness of matrices based on the ‘k-join’ of cubic cyclic graphs (for all k ∈ Z+). Basic tools are the representation theory of the symmetric group and geometric invariant theory, in particular the Hanlon-Wales theorem on the decomposition of Brauer algebras and the ProcesiSchwarz theorem on inequalities defining orbit spaces.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 121 شماره
صفحات -
تاریخ انتشار 2016