Congruences for Overpartition K-tuples
نویسنده
چکیده
An overpartition of the nonnegative integer n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a number may be overlined. Let k ≥ 1 be an integer. An overpartition k-tuple of a positive integer n is a k-tuple of overpartitions wherein all listed parts sum to n. Let pk(n) be the number of overpartition k-tuples of n. In this paper, we will give a short proof of Keister, Sellers and Vary’s theorem on congruences for pk(n) modulo powers of 2. We also obtain some congruences for pk(n) modulo prime ! and integer 2k.
منابع مشابه
Some Arithmetic Properties of Overpartition K -tuples
Abstract Recently, Lovejoy introduced the construct of overpartition pairs which are a natural generalization of overpartitions. Here we generalize that idea to overpartition ktuples and prove several congruences related to them. We denote the number of overpartition k-tuples of a positive integer n by pk(n) and prove, for example, that for all n ≥ 0, pt−1(tn + r) ≡ 0 (mod t) where t is prime a...
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