Abstract
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 ′−i−j+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 2t-core partitions of n are obtained. A simple convolution identity for t-cores is also given.
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Chen, S. Arithmetical properties of the number of t-core partitions. Ramanujan J 18, 103–112 (2009). https://doi.org/10.1007/s11139-007-9045-5
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DOI: https://doi.org/10.1007/s11139-007-9045-5