Congruences for bipartition and partition triples with 4-core
Article
First Online:
Received:
Accepted:
- 112 Downloads
Abstract
We prove some congruences for the number of bipartitions \(A_4(n)\) and partition triples \(B_4(n)\) of a positive integer n with 4-core.
Keywords
Bipartition Partition triples t-core partition CongruenceMathematics Subject Classification
11P83 05A15 05A17References
- 1.Baruah, N.D., Nath, K.: Infinite families of arithmetic identities for 4-cores. Bull. Aust. Math. Soc. 87, 304–315 (2013)MathSciNetCrossRefMATHGoogle Scholar
- 2.Baruah, N.D., Nath, K.: Infinite families of arithmetic identities and congruences for bipartitions with 3-cores. J. Number Theory. 149, 92–104 (2015)Google Scholar
- 3.Hirschhorn, M.D., Garvan, F., Borwein, J.: Cubic analogs of the Jacobian cubic theta function \(\theta (z, q)\). Can. J. Math. 45, 673–694 (1993)Google Scholar
- 4.Hirschhorn, M.D., Sellers, J.A.: Some amazing facts about 4-cores. J. Number Theory. 60, 51–69 (1996)MathSciNetCrossRefMATHGoogle Scholar
- 5.Hirschhorn, M.D., Sellers, J.A.: Two congruences involving 4-cores. Electron J. Combin. 3(2), R 10 (1996)Google Scholar
- 6.Lin, B.L.S.: Arithmetic properties of bipartitions with 3-core. J. Number Theory. 139, 44–52 (2014)MathSciNetCrossRefMATHGoogle Scholar
- 7.Wang, L.: Arithmetic identities and congruences for partition triples with 3-cores. arXiv:1502.06454
- 8.Xia, X.W.: Arithmetic properties of bipartitions with 3-core. Ramanujan J. doi: 10.1007/s11139-014-9643-y
Copyright information
© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2016