Abstract
In 1967, it was proved that the partitions of n into parts ≢ 0, ±l(mod 6) are equinumerous with partitions wherein the difference between parts is never 1, no part appears more than twice and no l’s appear. Polynomial generating functions related to this theorem have useful and interesting representations involving Gaussian polynomials and q-trinomial coefficients.
Partially supported by National Science Foundation Grant DMS 8702695–04.
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References
AK. Agarwal and G. E. Andrews, Hook differences and lattice paths, J. Planning and Stat. Inf. 14 (1986), 5–14.
G. E. Andrews, Some new partition theorems, J. Comb. Th. 2 (1967), 431–436.
—Some new partition theorems II, J. Comb. Th. 7 (1969), 262–263.
—A new property of partitions with applications to the Rogers-Ramanujan identities, J. Comb. Th. 10 (1971), 266–270.
—The Theory of Partitions, Encyclopedia of Math, and Its Appl., Vol. 2, G.-C. Rota, ed., Addison-Wesley, Reading, 1976 (Reprinted: Cambridge University Press, London, 1985).
Euler’s “Exemplum memorabile inductionis fallacis” and q-trinomial coefficients, J. Amer. Math. Soc. 3 (1990), 653–669.
G. E. Andrews and R. J. Baxter, Lattice gas generalizations of the hard hexagon model, III. q-trinomial coefficients, J. of Stat. Physics 47 (1987), 297–330.
N. J. Fine, Basic Hypergeometric Series and Applications, Math Surveys and Monographs, No. 27, Amer. Math. Soc., Providence 1988.
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© 1996 Birkhäuser Boston
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Andrews, G.E. (1996). Rogers-Ramanujan polynomials for modulus 6. In: Berndt, B.C., Diamond, H.G., Hildebrand, A.J. (eds) Analytic Number Theory. Progress in Mathematics, vol 138. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4086-0_2
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DOI: https://doi.org/10.1007/978-1-4612-4086-0_2
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