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Dichromatic Polynomials and Potts Models Summed Over Rooted Maps
R.J. Baxter
School of Mathematical Sciences and Research School of Physical Sciences and Engineering, Australian National University, Canberra, A.C.T. 0200, Australia
Annals of Combinatorics 5(1) p.17-36 March, 2001
AMS Subject Classification: 05C15, 82B20
We consider the sum of dichromatic polynomials over non-separable rooted planar maps, an interesting special case of which is the enumeration of such maps. We present some known results and derive new ones. The general problem is equivalent to the q-state Potts model randomized over such maps: it remains an open question whether this model exhibits a phase transition or critical behaviour.
Keywords: graph theory, statistical mechanics, dichromatic polynomials, lattice models, Potts model, phase transitions


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