Related papers: A statistical mechanical approach to restricted in…
Steingrimsson has recently introduced a partition analogue of Foata-Zeilberger's mak statistic for permutations and conjectured that its generating function is equal to the classical q-Stirling numbers of second kind. In this paper we prove…
In statistical physics and information theory, although the exponent of the partition function is often of our primary interest, there are cases where one needs more detailed information. In this paper, we present a general framework to…
We derive continued fractions for partition generating functions, utilizing both Euler's techniques and Ramanujan's techniques. Although our results are for integer partitions there is scope to extend this work to vector partitions,…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
We propose a simple estimator that allows to calculate the absolute value of a system's partition function from a finite sampling of its canonical ensemble. The estimator utilizes a volume correction term to compensate the effect that the…
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
Let $\mathcal{A}=\left(a_i\right)_{i=1}^\infty$ be a weakly increasing sequence of positive integers and let $k$ be a fixed positive integer. For an arbitrary integer $n$, the restricted partition $p_\mathcal{A}(n,k)$ enumerates all the…
We present the path integral representation of the generating function for classical exclusive particle systems. By introducing hard-core bosonic creation and annihilation operators and appropriate commutation relations, we construct the…
We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…
We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…
The algebra of symmetric functions contains several interesting families of symmetric functions indexed by integer partitions or skew partitions. Given a sequence $\{u_n\}$ of symmetric functions taken from one of these families such that…
We develop a new closed-form arithmetic and recursive formula for the partition function and a generalization of Andrews' smallest parts (spt) function. Using the inclusion-exclusion principle, we additionally develop a formula for the…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Proposed is an alternative method for permutational sampling in quantum gases using the path integral formulation of statistical mechanics. It is shown that in principle we are able to use two operators which enable us to construct a Markov…
In this note we will give various exact formulas for functions on integer partitions including the functions $p(n)$ and $p(n,k)$ of the number of partitions of $n$ and the number of such partitions into exactly $k$ parts respectively. For…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
We obtain an asymptotic expansion for $p(n)$, the number of partitions of a natural number $n$, starting from a formula that relates its generating function $f(t), t\in (0,1)$ with the characteristic functions of a family of sums of…
We describe the statistical mechanics of a new method to produce very cold atoms or molecules. The method results from trapping a gas in a potential well, and sweeping through the well a semi-permeable barrier, one that allows particles to…
We consider procedures of sampling parts from a random integer partition. We determine asymptotically the probabilty distribution of the randomly-selected part whenever the positive integer that is partitioned becomes large.
We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in…