Related papers: Spin Multiplicities

Here we examine the number of ways to partition an integer $n$ into $k$th powers when $n$ is large. Simplified proofs of some asymptotic results of Wright are given using the saddle-point method, including exact formulas for the expansion…

The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fields of modular forms. The observations suggest certain patterns, which deserve further…

The paper presents a discussion on the asymptotic formula for the number of plane partitions of a large positive integer.

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

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vign\'{e}ras multiple gamma functions by considering the classical limit of the multiple…

We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.

We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions…

We give new bounds and asymptotic estimates on the largest Kronecker and induced multiplicities of finite groups. The results apply to large simple groups of Lie type and other groups with few conjugacy classes.

We use new bounds of double exponential sums with ratios of integers from prescribed intervals to get an asymptotic formula for the number of solutions to congruences $$ \sum_{j=1}^n a_j x_jy_j^{-1} \equiv a_0 \pmod p, $$ with variables…

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…

It is experimentally demonstrated that with multi-frequency excitation of weak amplitude the dynamics of a cluster of dipolar-coupled spins can be manipulated to perform parallel logic operations with long bit arrays.

Consider an integral $I(s):=\int_0^T e^{-s(x^2-icx)}dx$, where $c>0$ and $T>0$ are arbitrary positive constants. It is proved that $I(s)\sim \frac{i}{sc}$ as $s\to +\infty$. The asymptotic behavior of the integral…

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vign\'{e}ras multiple gamma function by considering the classical limit of the multiple q-gamma…

In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Schr"odinger equations in one space dimension. It turns out that for a system there exists a small solution of which asymptotic…

We prove an explicit formula to count the partitions of $n$ whose product of the summands is at most $n$. In the process, we also deduce a result to count the multiplicative partitions of $n$.

We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.

Spinons are among the generic excitations in one-dimensional spin systems, they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show…

Asymptotic formulas of the number of various partitions are studied, like 3-colored partitions, concave partitions, certain plane partitions, partitions without small parts, the number of p-rings.

This work gives a general approach to the determination of the asymptotic behavior of the sums of functions of primes based on the distribution of primes. It refines the estimate of the remainder term of the asymptotic expansion of the sums…

We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the…