首页|Proofs of Some Conjectures of Andrews and Paule on 2-Elongated Plane Partitions
Proofs of Some Conjectures of Andrews and Paule on 2-Elongated Plane Partitions
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Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function dk(n)and proved a large number of results on dk(n)with k=2,3.In particular,they posed some conjectures on congruences modulo powers of 3 for d2(n).Their work has attracted the attention of da Silva,Hirschhorn,Sellers and Smoot.Very recently,Smoot proved a congruence family for d2(n)which implies one conjecture due to Andrews and Paule by using the localization method.In this paper,we prove the rest two conjectures given by Andrews and Paule.
partitionscongruences2-elongated plane partitionstheta function identities
Olivia X.M.YAO
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School of Mathematical Sciences,Suzhou University of Science and Technology,Jiangsu 215009,P.R.China
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