For a given set A of nonnegative integers the representation functions R2(A, n), R3(A, n) are defined as the number of solutions of the equation n = x+y, x, y ∈ A with condition x <y, x \leq y respectively. In this note we are going to determine the partitions of natural numbers into two parts such that their representation functions are the same from a certain point onwards
We present two analogues of two well-known elementary arguments for a lower bound for p(n), the numb...
Abstract. We give a series of recursive identities for the number of partitions with exactly k parts...
The first chapter examines $p_b(n)$, the number of partitions of $n$ into powers of $b$, along with ...
For a given set A of nonnegative integers the representation functions R2(A, n), R3(A, n) are define...
AbstractTextFor any given two positive integers k1 and k2, and any set A of nonnegative integers, le...
For a set of nonnegative integers S let RS(n) denote the number of unordered representations of the ...
AbstractLet A be an infinite subset of natural numbers, n∈N and X a positive real number. Let r(n) d...
AbstractLet A={a1,a2,…}(a1<a2<⋯) be an infinite sequence of nonnegative integers. Let k≥2 be a fixed...
Let p(n) denote the number of partitions of the integer n. The first exact formula for p(n) was publ...
A nonrecursive, finite, exact integer partition function \(p(n)\) is presented in terms of elementar...
A partition of a positive number n is a representation of this number as a sum of natural numbers, c...
AbstractFor a set A of positive integers and any positive integer n, let R1(A,n), R2(A,n) and R3(A,n...
Partition function P(n) is defined as the number of ways that a positive integer can be expressed as...
AbstractLet n = n1 + n2 + … + nj a partition Π of n. One will say that this partition represents the...
Three classical results concern the number of representations of the positive integer n in the form ...
We present two analogues of two well-known elementary arguments for a lower bound for p(n), the numb...
Abstract. We give a series of recursive identities for the number of partitions with exactly k parts...
The first chapter examines $p_b(n)$, the number of partitions of $n$ into powers of $b$, along with ...
For a given set A of nonnegative integers the representation functions R2(A, n), R3(A, n) are define...
AbstractTextFor any given two positive integers k1 and k2, and any set A of nonnegative integers, le...
For a set of nonnegative integers S let RS(n) denote the number of unordered representations of the ...
AbstractLet A be an infinite subset of natural numbers, n∈N and X a positive real number. Let r(n) d...
AbstractLet A={a1,a2,…}(a1<a2<⋯) be an infinite sequence of nonnegative integers. Let k≥2 be a fixed...
Let p(n) denote the number of partitions of the integer n. The first exact formula for p(n) was publ...
A nonrecursive, finite, exact integer partition function \(p(n)\) is presented in terms of elementar...
A partition of a positive number n is a representation of this number as a sum of natural numbers, c...
AbstractFor a set A of positive integers and any positive integer n, let R1(A,n), R2(A,n) and R3(A,n...
Partition function P(n) is defined as the number of ways that a positive integer can be expressed as...
AbstractLet n = n1 + n2 + … + nj a partition Π of n. One will say that this partition represents the...
Three classical results concern the number of representations of the positive integer n in the form ...
We present two analogues of two well-known elementary arguments for a lower bound for p(n), the numb...
Abstract. We give a series of recursive identities for the number of partitions with exactly k parts...
The first chapter examines $p_b(n)$, the number of partitions of $n$ into powers of $b$, along with ...
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