AbstractLet p(n) be the number of partitions of a non-negative integer n. In this paper we prove that for any progression r (mod t), and for large X, we have 1.(a) The number of n ≤ X such that n ≡ r (mod t) and p(n) is even is ⪢ √X, and2.(b) The number of n ≤ X such that n ≡ r (mod t) and p(n) is odd is ⪢ √Xlog X, provided that one such n exists
In recent years, numerous functions which count the number of parts of various types of partitions h...
AbstractMaking use of an identity of Euler's involving the partition function p(n), Kolberg (Math. S...
AbstractLet p(n) denote the number of partitions of an integer n. Recently, the author has shown tha...
AbstractLet p(n) be the number of partitions of a non-negative integer n. In this paper we prove tha...
Abstract.Let S denote a subset of the positive integers, and let pS(n) be the associated partition f...
AbstractLet N be the set of all positive integers and D a subset of N. Let p(D,n) be the number of p...
The parity of p(n), the ordinary partition function, has been studied for at least a century, yet it...
The parity of p(n), the ordinary partition function, has been studied for at least a century, yet it...
Recently, Hirschhorn and the first author considered the parity of the function a(n) which counts th...
AbstractAlthough much is known about the partition function, little is known about its parity. For t...
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
Abstract. Working in the ring A of formal power series in one variable over the field of two element...
© 2017 World Scientific Publishing Company. We study νk(n), the number of partitions of n into k par...
In recent years, numerous functions which count the number of parts of various types of partitions h...
A partition of a non-negative integer n is any non-increasing sequence of positive integers whose su...
In recent years, numerous functions which count the number of parts of various types of partitions h...
AbstractMaking use of an identity of Euler's involving the partition function p(n), Kolberg (Math. S...
AbstractLet p(n) denote the number of partitions of an integer n. Recently, the author has shown tha...
AbstractLet p(n) be the number of partitions of a non-negative integer n. In this paper we prove tha...
Abstract.Let S denote a subset of the positive integers, and let pS(n) be the associated partition f...
AbstractLet N be the set of all positive integers and D a subset of N. Let p(D,n) be the number of p...
The parity of p(n), the ordinary partition function, has been studied for at least a century, yet it...
The parity of p(n), the ordinary partition function, has been studied for at least a century, yet it...
Recently, Hirschhorn and the first author considered the parity of the function a(n) which counts th...
AbstractAlthough much is known about the partition function, little is known about its parity. For t...
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
Abstract. Working in the ring A of formal power series in one variable over the field of two element...
© 2017 World Scientific Publishing Company. We study νk(n), the number of partitions of n into k par...
In recent years, numerous functions which count the number of parts of various types of partitions h...
A partition of a non-negative integer n is any non-increasing sequence of positive integers whose su...
In recent years, numerous functions which count the number of parts of various types of partitions h...
AbstractMaking use of an identity of Euler's involving the partition function p(n), Kolberg (Math. S...
AbstractLet p(n) denote the number of partitions of an integer n. Recently, the author has shown tha...
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