Abstract
In this paper, we present bijective proofs of several identities involving partitions by making use of a new way for representing partitions as two-line matrices. We also apply these ideas to give a combinatorial proof for an identity related to three-quadrant Ferrers graphs.
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Andrews, G.E.: Enumerative proofs of certains q-identities. Glasg. Math. J. 8, 33–40 (1967)
Andrews, G.E.: Ramanujan’s “lost” notebook I, partial θ-functions. Adv. Math. 41, 137–172 (1981)
Andrews, G.E.: Three-quadrant Ferrers graphs. Indian J. Math. 42, 1–7 (2000)
Andrews, G.E., Berndt, B.C.: Ramanujan’s Lost Notebook, Part I. Springer, New York (2005)
Berndt, B.C.: Number Theory in the Spirit of Ramanujan. AMS, Providence (2006)
Little, D.P., Sellers, J.A.: New proofs of identities of Lebesgue and Göllnitz via Tilings. J. Comb. Theory, Ser. A 116, 223–231 (2009)
Pak, I.: Partition bijections, a survey. Ramanujan J. 12, 5–75 (2006)
Santos, J.P.O., Silva, R.: A combinatorial proof for an identity involving partitions with distinct odd parts. South East Asian J. Math. Math. Sci. (accepted)
Santos, J.P.O., Mondek, P., Ribeiro, A.C.: New two-line arrays representing partitions. Ann. Comb. (accepted)
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Dedicated to George Andrews for his 70th birthday
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Brietzke, E.H.M., Santos, J.P.O. & da Silva, R. Bijective proofs using two-line matrix representations for partitions. Ramanujan J 23, 265–295 (2010). https://doi.org/10.1007/s11139-009-9207-8
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DOI: https://doi.org/10.1007/s11139-009-9207-8