Abstract
The parity of g(n) and h(n), the enumerators of restricted partitions of n appearing in the Rogers-Ramanujan identities, is studied. The parity of g(n) for odd n and that of h(n) for even n are completely determined. It is shown that these numbers are almost always even.
Mathematics Subject Classification: Primary 11P83, 11F11 and 11E12
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Reference
G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its Applications, Addison-Wesley 1976.
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Gordon, B. (2012). On the Parity of the Rogers-Ramanujan Coefficients. In: Alladi, K., Garvan, F. (eds) Partitions, q-Series, and Modular Forms. Developments in Mathematics, vol 23. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0028-8_8
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DOI: https://doi.org/10.1007/978-1-4614-0028-8_8
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