We discuss a family of restricted m-ary overpartition functions bm,j （n）, which is the number of m-ary overpartitions of n with at most i ＋ j copies of the non-overlined part m^i allowed, and obtain a family of con...We discuss a family of restricted m-ary overpartition functions bm,j （n）, which is the number of m-ary overpartitions of n with at most i ＋ j copies of the non-overlined part m^i allowed, and obtain a family of congruences for bm,lm-1 （n）.展开更多
Let P-3 （n） be the number of overpartition triples of n. By elementary series manipulations, we establish some congruences for P-3（n） modulo small powers of 2, such as P-3（16n＋14）≡0 （mod 32）, P-3（8n＋7）≡0...Let P-3 （n） be the number of overpartition triples of n. By elementary series manipulations, we establish some congruences for P-3（n） modulo small powers of 2, such as P-3（16n＋14）≡0 （mod 32）, P-3（8n＋7）≡0 （mod 64）.We also find many arithmetic properties for P-3（n） modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences： for any integers α≥1 and n ≥ 0, we have展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.s1077110010871166)+2 种基金the Natural Science Foundation of Jiangsu Province (Grant No.BK2007030)the Natural Science Foundation of Jiangsu Educational Committee (Grant No.s06KJD11017907KJD110207)
文摘We discuss a family of restricted m-ary overpartition functions bm,j （n）, which is the number of m-ary overpartitions of n with at most i ＋ j copies of the non-overlined part m^i allowed, and obtain a family of congruences for bm,lm-1 （n）.
文摘Let P-3 （n） be the number of overpartition triples of n. By elementary series manipulations, we establish some congruences for P-3（n） modulo small powers of 2, such as P-3（16n＋14）≡0 （mod 32）, P-3（8n＋7）≡0 （mod 64）.We also find many arithmetic properties for P-3（n） modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences： for any integers α≥1 and n ≥ 0, we have
