Proofs of Some Conjectures of Andrews and Paule on 2-Elongated Plane Partitions  

作　　者：Olivia X.M.YAO 

机构地区：[1]School of Mathematical Sciences,Suzhou University of Science and Technology,Jiangsu 215009,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第6期735-740,共6页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12371334);the Natural Science Foundation of Jiangsu Province(Grant No.BK20221383)。

摘　　要：Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function d_(k)(n)and proved a large number of results on d_(k)(n)with k=2,3.In particular,they posed some conjectures on congruences modulo powers of 3 for d_(2)(n).Their work has attracted the attention of da Silva,Hirschhorn,Sellers and Smoot.Very recently,Smoot proved a congruence family for d_(2)(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.

关 键 词：PARTITIONS CONGRUENCES 2-elongated plane partitions theta function identities 

分 类 号：O15[理学—数学]