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Antihook differences and some partition identities


Author: A. K. Agarwal
Journal: Proc. Amer. Math. Soc. 110 (1990), 1137-1142
MSC: Primary 11P81; Secondary 05A17
DOI: https://doi.org/10.1090/S0002-9939-1990-1023341-X
MathSciNet review: 1023341
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Abstract | References | Similar Articles | Additional Information

Abstract: Anti-hook differences are applied to give new combinatorial interpretations to three identities from Slater's Compendium.


References [Enhancements On Off] (What's this?)

  • [1] A. K. Agarwal, Rogers-Ramanujan identities for $ n$-color partitions, J. Number Theory 28 (1988), 299-305. MR 932378 (89b:11080)
  • [2] A. K. Agarwal and G. E. Andrews, Hook-differences and lattice paths, J. Statist. Plann. Inference 14 (1986), 5-14. MR 845909 (87k:05017)
  • [3] -, Rogers-Ramanujan identities for partitions with "$ N$ copies of $ N$," J. Combin. Theory Ser. Ser. A.
  • [4] F. G. Dyson, Some guesses in the theory of partitions, Eureka (Cambridge) 8 (1944), 10-15.
  • [5] L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1884), 318-343.
  • [6] L. J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 54 (1952), 147-167. MR 0049225 (14:138e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1023341-X
Keywords: Partitions, anti-hook differences, combinatorial identities, Frobenius's notation
Article copyright: © Copyright 1990 American Mathematical Society

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