Related papers: On the integer partitions recursive structure

Let $p_n$ be the number of partitions of an integer $n$. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting…

A partition polynomial is a refinement of the partition number p(n) whose coefficients count some special partition statistic. Just as partition numbers have useful asymptotics so do partition polynomials. In fact, their asymptotics…

The novel notion of rigid commutators is introduced to determine the sequence of the logarithms of the indices of a certain normalizer chain in the Sylow 2-subgroup of the symmetric group on 2^n letters. The terms of this sequence are…

A class of associative (super) algebras is presented, which naturally generalize both the symmetric algebra $Sym(V)$ and the wedge algebra $\wedge (V)$, where $V$ is a vector-space. These algebras are in a bijection with those subsets of…

For a set of nonnegative integers $S$ let $R_{S}(n)$ denote the number of unordered representations of the integer $n$ as the sum of two different terms from $S$. In this paper we focus on partitions of the natural numbers into two sets…

This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…

Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative…

Recently, Andrews introduced separable integer partition classes and studied some well-known theorems. In this article, we will consider the types of partitions with restrictions on consecutive parts. We will show that such partitions are…

We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.

In a recent paper (Tran et al., Ann.Phys.311(2004)204), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We…

An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found

Zeckendorf proved that every positive integer has a unique partition as a sum of non-consecutive Fibonacci numbers. We study the difference between the number of summands in the partition of two consecutive integers. In particular, let…

In this short note we present a class of conjectures on partitions of integers as summations of primes, which are extensions of Goldbach conjecture.

An integer partition \lambda of n corresponds, via its Ferrers diagram, to an artinian monomial ideal I of colength n in the polynomial ring on two variables. If the partition \lambda corresponds to an integrally closed ideal we call…

We apply the geometric construction of solutions of some variational problems of combinatorics to estimate the number of partitions and of plane partitions of an integer.

In this paper, we consider representations of integers as sums of at most four distinct $m$-gonal numbers (allowing a fixed number of repeats of each polygonal number occurring in the sum). We show that the number of such representations…

The main aim of this paper is twofold: (1) Suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions --- a way of writing an…

In this article we obtain an explicit formula in terms of the partitions of the positive integer $n$ to express the $n$-th term of a wide class of sequences of numbers defined by recursion. Our proof is based only on arithmetics. We compare…

The Fibonacci numbers are the prototypical example of a recursive sequence, but grow too quickly to enumerate sets of integer partitions. The same is true for the other classical sequences $a(n)$ defined by Fibonacci-like recursions: the…

In this paper, the relation between the integer partition theory and a kind of rational solution of the dispersion long wave equations is studied. For the integer partition {\lambda}= ({\lambda}1,{\lambda}2,... ,{\lambda}n) of positive…