Partitions of ℤm with the same representation functions
نویسندگان
چکیده
For A ⊆ Zm and n ∈ Zm, let σ1(A, n), σ2(A, n), σ3(A, n) denote the number of solutions of the equation n = a+a′ with ordered pairs (a, a′) ∈ A, unordered pairs (a, a′) ∈ A(a = a′) and unordered pairs (a, a′) ∈ A, respectively. In this paper, for any i ∈ {1, 2, 3}, we determine all subsets A of Zm such that σi(A, n) = σi(Zm\A, n) holds for all n ∈ Zm.
منابع مشابه
Partitions of Natural Numbers and Their Representation Functions
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 53 شماره
صفحات -
تاریخ انتشار 2012