Counting non-planar diagrams: an exact formula |
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| Institution: | 1. School of Information Sciences and Technology, Chukyo University, Toyota 470-0393, Japan;2. School of International Liberal Studies, Chukyo University, Nagoya 466-8666, Japan;3. Graduate School of Natural Sciences, Nagoya City University, Nagoya 467-8501, Japan;4. Institute of Advanced Studies in Artificial Intelligence, Chukyo University, Toyota 470-0393, Japan;1. IMECC/UNICAMP, R. Sérgio Buarque de Holanda 651, Cidade Universitária “Zeferino Vaz”, 13083-859, Campinas, SP, Brazil;2. Instituto Federal de São Paulo, Av. Comendador Aladino Selmi, s/no Prédio 4 CTI Renato Archer, 13069-901, Campinas, SP, Brazil;1. Université Clermont Auvergne, LIMOS, CNRS, France;2. Université de Lille, CRIStAL, CNRS, INRIA, France |
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| Abstract: | We present an explicit solution of a simply stated, yet unsolved, combinatorial problem, of interest both in quantum field theory (Feynman diagrams enumeration, beyond the planar approximation) and in statistical mechanics (high temperature loop expansion of some frustrated lattice spin model). |
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