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Rogers-Ramanujan identities in the hard hexagon model. (English) Zbl 0511.05004
MSC:
05A19Combinatorial identities, bijective combinatorics
82B05Classical equilibrium statistical mechanics (general)
33D15Basic hypergeometric functions of one variable, r φ s
References:
[1]R. J. Baxter,J. Phys. A: Math. Gen. 13:L61 (1980). · doi:10.1088/0305-4470/13/3/007
[2]R. J. Baxter,Exactly Solved Models in Statistical Mechanics, Chap. 14, (to be published by Academic, London, 1981/2).
[3]D. S. Gaunt and M. E. Fisher,J. Chem. Phys. 43:2840 (1965). · doi:10.1063/1.1697217
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[7]S. K. Tsang,J. Stat. Phys. 20:95 (1979). · doi:10.1007/BF01013748
[8]R. J. Baxter,J. Math. Phys. 9:650 (1968). · doi:10.1063/1.1664623
[9]S. B. Kelland,Can. J. Phys. 54:1621 (1976).
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[11]R. J. Baxter and S. K. Tsang,J. Phys. A: Math. Gen. 13:1023 (1980). · doi:10.1088/0305-4470/13/3/035
[12]R. J. Baxter, Exactly Solved Models, inFundamental Problems in Statistical Mechanics V, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1980).
[13]L. J. Slater,Generalized Hypergeometric Functions (Cambridge University Press, Cambridge, 1966).
[14]G. E. Andrews,The Theory of Partitions, Chap. 7 (Addison-Wesley, Reading, Massachusetts, 1976).
[15]L. J. Rogers,Proc. London Math. Soc. (1),25:318 (1894). · doi:10.1112/plms/s1-25.1.318
[16]S. Ramanujan,Proc. Cambridge Philos. Soc. 19:214 (1919).
[17]B. J. Birch,Math. Proc. Cambridge Philos. Soc. 78:73 (1975). · Zbl 0305.10002 · doi:10.1017/S0305004100051501
[18]L. J. Rogers,Proc. London Math. Soc. (2),19:387 (1921). · doi:10.1112/plms/s2-19.1.387
[19]G. E. Andrews, The Hard-Hexagon Model and New Rogers-Ramanujan Type Identities, Dept. Math. Research Report 8167, Pennsylvania State University (1981).
[20]I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series and Products (Academic, New York, 1965).
[21]M. N. Barber and R. J. Baxter,J. Phys. C: Solid State Phys. 6:2913 (1973). · doi:10.1088/0022-3719/6/20/004
[22]L. J. Slater,Proc. London Math. Soc. (2),54:147 (1951). · Zbl 0046.27204 · doi:10.1112/plms/s2-54.2.147
[23]G. N. Watson,J. Indian Math. Soc. 20:57 (1933).