Some identities involving the partition function
نویسندگان
چکیده
منابع مشابه
Some families of identities for the integer partition function
We give a series of recursive identities for the number of partitions with exactly k parts and with constraints on both the minimal difference among the parts and the minimal part. Using these results, we demonstrate that the number of partitions of n is equal to the number of partitions of 2n + d ( n 2 ) of length n, with d-distant parts. We also provide a direct proof for this identity. This ...
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For any positive integer n and fixed integer t ≥ 1, we define function Ut(n) = min{k : 1 t + 2 t + · · · + n t + k = m, n | m, k ∈ N + , t ∈ N + }, where n ∈ N + , m ∈ N + , which is a new pseudo Smarandache function. The main purpose of this paper is using the elementary method to study the properties of Ut(n), and obtain some interesting identities involving function Ut(n). In reference [1], ...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1957
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10492