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Some Arithmetic Properties of Overpartition k-Tuples
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Published/Copyright:
June 15, 2009
Abstract
Recently, Lovejoy introduced the construct of overpartition pairs which are a natural generalization of overpartitions. Here we generalize that idea to overpartition k-tuples and prove several congruences related to them. We denote the number of overpartition k-tuples of a positive integer n by 
k(n) and prove, for example, that for all n ≥ 0,
t–1(tn + r) ≡ 0 (mod t)
where t is prime and r is a quadratic nonresidue mod t.
Received: 2008-09-04
Accepted: 2009-03-02
Published Online: 2009-06-15
Published in Print: 2009-June
© de Gruyter 2009
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- Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
- On Newman's Conjecture and Prime Trees
- The Dying Rabbit Problem Revisited
- A Note on the q-Binomial Rational Root Theorem
- The 3x + 1 Conjugacy Map over a Sturmian Word
- The Number of Relatively Prime Subsets of {1, 2, . . . , n}
- Generalized Levinson–Durbin Sequences and Binomial Coefficients
- Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- Some Arithmetic Properties of Overpartition k-Tuples
- Characterizations of Midy's Property
Articles in the same Issue
- Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
- On Newman's Conjecture and Prime Trees
- The Dying Rabbit Problem Revisited
- A Note on the q-Binomial Rational Root Theorem
- The 3x + 1 Conjugacy Map over a Sturmian Word
- The Number of Relatively Prime Subsets of {1, 2, . . . , n}
- Generalized Levinson–Durbin Sequences and Binomial Coefficients
- Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- Some Arithmetic Properties of Overpartition k-Tuples
- Characterizations of Midy's Property
