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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baruah, N.D., Nath, K.: Infinite families of arithmetic identities for 4-cores. Bull. Aust. Math. Soc. 87, 304–315 (2013)
Baruah, N.D., Nath, K.: Infinite families of arithmetic identities and congruences for bipartitions with 3-cores. J. Number Theory. 149, 92–104 (2015)
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)
Hirschhorn, M.D., Sellers, J.A.: Some amazing facts about 4-cores. J. Number Theory. 60, 51–69 (1996)
Hirschhorn, M.D., Sellers, J.A.: Two congruences involving 4-cores. Electron J. Combin. 3(2), R 10 (1996)
Lin, B.L.S.: Arithmetic properties of bipartitions with 3-core. J. Number Theory. 139, 44–52 (2014)
Wang, L.: Arithmetic identities and congruences for partition triples with 3-cores. arXiv:1502.06454
Xia, X.W.: Arithmetic properties of bipartitions with 3-core. Ramanujan J. doi:10.1007/s11139-014-9643-y
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Saikia, N., Boruah, C. Congruences for bipartition and partition triples with 4-core. Afr. Mat. 28, 199–206 (2017). https://doi.org/10.1007/s13370-016-0437-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13370-016-0437-9