Combinatorics and physics

Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics.

"Combinatorial Physics is an emerging area which unites combinatorial and discrete mathematical techniques applied to theoretical physics, especially Quantum Theory.".

"Physical combinatorics might be defined naively as combinatorics guided by ideas or insights from physics".

See also

• Mathematical physics
• Statistical physics
• Ising model
• Percolation theory
• Tutte polynomial
• Partition function
• Hopf algebra
• Combinatorics and dynamical systems
• Bit-string physics
• Combinatorial hierarchy
• Quantum theory

Further reading

• Some Open Problems in Combinatorial Physics, G. Duchamp, H. Cheballah
• One-parameter groups and combinatorial physics, G. Duchamp, K.A. Penson, A.I. Solomon, A.Horzela, P.Blasiak
• Combinatorial Physics, Normal Order and Model Feynman Graphs, A.I. Solomon, P. Blasiak, G. Duchamp, A. Horzela, K.A. Penson
• Hopf Algebras in General and in Combinatorial Physics: a practical introduction, G. Duchamp, P. Blasiak, A. Horzela, K.A. Penson, A.I. Solomon
• Discrete and Combinatorial Physics
• Bit-String Physics: a Novel "Theory of Everything", H. Pierre Noyes
• Combinatorial Physics, Ted Bastin, Clive William Kilmister, World Scientific, 1995, ISBN 9810222122

• Physical Combinatorics and Quasiparticles, Giovanni Feverati, Paul A. Pearce, Nicholas S. Witte
• Physical Combinatorics of Non-Unitary Minimal Models, Hannah Fitzgerald
• Paths, Crystals and Fermionic Formulae, G.Hatayama, A.Kuniba, M.Okado, T.Takagi, Z.Tsuboi
• On powers of Stirling matrices, Istvan Mezo

• "On cluster expansions in graph theory and physics", N BIGGS - The Quarterly Journal of Mathematics, 1978 - Oxford Univ Press

• Enumeration Of Rational Curves Via Torus Actions, Maxim Kontsevich, 1995
• Non-commutative Calculus and Discrete Physics, Louis H. Kauffman, February 1, 2008
• Sequential cavity method for computing free energy and surface pressure, David Gamarnik, Dmitriy Katz, July 9, 2008

Combinatorics and statistical physics

• "Graph Theory and Statistical Physics", J.W. Essam, Discrete Mathematics, 1, 83-112 (1971).
• Combinatorics In Statistical Physics
• Hard Constraints and the Bethe Lattice: Adventures at the Interface of Combinatorics and Statistical Physics, Graham R. Brightwell Peter Winkler
• Graphs, Morphisms, and Statistical Physics: DIMACS Workshop Graphs, Morphisms and Statistical Physics, March 19-21, 2001, DIMACS Center, Jaroslav Nešetřil, Peter Winkler, AMS Bookstore, 2001, ISBN 0821835513

Conference proceedings

• Proc. of Combinatorics and Physics, Los Alamos, August 1998

• Physics and Combinatorics 1999: Proceedings of the Nagoya 1999 International Workshop, Anatol N. Kirillov, Akihiro Tsuchiya, Hiroshi Umemura, World Scientific, 2001, ISBN 9810245785

• Physics and combinatorics 2000: proceedings of the Nagoya 2000 International Workshop, Anatol N. Kirillov, Nadejda Liskova, World Scientific, 2001, ISBN 9810246420

• Asymptotic combinatorics with applications to mathematical physics: a European mathematical summer school held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001, Anatoliĭ, Moiseevich Vershik, Springer, 2002, ISBN 3540403124

• Counting Complexity: An International Workshop On Statistical Mechanics And Combinatorics, 10–15 July 2005, Dunk Island, Queensland, Australia

• Proceedings of the Conference on Combinatorics and Physics, MPIM Bonn, March 19-23, 2007