The Ramanujan Journal

, Volume 18, Issue 1, pp 103–112 | Cite as

Arithmetical properties of the number of t-core partitions

  • Shichao Chen


Let Λ={λ 1⋅⋅⋅λ s ≥1} be a partition of an integer n. Then the Ferrers-Young diagram of Λ is an array of nodes with λ i nodes in the ith row. Let λ j ′ denote the number of nodes in column j in the Ferrers-Young diagram of Λ. The hook number of the (i,j) node in the Ferrers-Young diagram of Λ is denoted by H(i,j):=λ i +λ j ′−ij+1. A partition of n is called a t-core partition of n if none of the hook numbers is a multiple of t. The number of t-core partitions of n is denoted by a(t;n). In the present paper, some congruences and distribution properties of the number of 2 t -core partitions of n are obtained. A simple convolution identity for t-cores is also given.


t-core partition Congruence Modular form 

Mathematics Subject Classification (2000)



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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsHenan UniversityHenanChina

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