Abstract
In his famous book “Combinatory Analysis” MacMahon introduced Partition Analysis as a computational method for solving problems in connection with linear homogeneous diophantine inequalities and equations, respectively. The object of this paper is to introduce an entirely new application domain for MacMahon’s operator technique. Namely, we show that Partition Analysis can be also used for proving hypergeometric multisum identities. Our examples range from combinatorial sums involving binomial coefficients, harmonic and derangement numbers to multisums which arise in physics and which are related to the Knuth-Bender theorem.
Partially supported by the visiting researcher program of the J. Kepler University Linz.
Supported by SFB-grant F1305 of the Austrian FWF.
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© 2001 Springer-Verlag Berlin Heidelberg
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Andrews, G.E., Paule, P. (2001). MacMahon’s Partition Analysis IV: Hypergeometric Multisums. In: Foata, D., Han, GN. (eds) The Andrews Festschrift. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56513-7_9
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DOI: https://doi.org/10.1007/978-3-642-56513-7_9
Publisher Name: Springer, Berlin, Heidelberg
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