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Transactions of the American Mathematical Society

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Hall-Littlewood functions, plane partitions, and the Rogers-Ramanujan identities


Author: John R. Stembridge
Journal: Trans. Amer. Math. Soc. 319 (1990), 469-498
MSC: Primary 05A19; Secondary 05A17, 05A30, 11P68
DOI: https://doi.org/10.1090/S0002-9947-1990-0986702-5
MathSciNet review: 986702
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Abstract: We apply the theory of Hall-Littlewood functions to prove several multiple basic hypergeometric series identities, including some previously known generalizations of the Rogers-Ramanujan identities due to G. E. Andrews and D. M. Bressoud. The techniques involve the adaptation of a method due to I. G. Macdonald for calculating partial fraction expansions of certain types of symmetric formal power series. Macdonald originally used this method to prove a pair of generating function identities for plane partitions conjectured by MacMahon and Bender-Knuth. We show that this method can also be used to prove another pair of plane partition identities recently obtained by R. A. Proctor.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0986702-5
Article copyright: © Copyright 1990 American Mathematical Society

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