Abstract
In this short note we prove a general partition theorem involving partitions with "N copies of N". These partitions arise in the Study of Hard-Hexagon Model and have recently been studied in [1]. To exhibit the importance of our main theorem we present three particular cases which yield elegant partition identities of Rogers-Ramanujan Type. We shall also pose a very significant open problem.
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References
A.K. Agarwal and G.E. Andrews, Rogers-Ramanujan Identities for Partitions with "N copies of N" (Communicated).
L.J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. 54 (1951–52), pp. 147–167.
W.N. Bailey, On the simplification of some identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (3) 1, (1951), pp. 217–221.
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© 1986 Springer-Verlag
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Agarwal, A.K. (1986). Partitions with "N copies of N". In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072504
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DOI: https://doi.org/10.1007/BFb0072504
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