相关论文: On Explicit Formula for Restricted Partition Funct…
In this article, we provide partition-theoretic interpretations for some new truncated pentagonal number theorem and identities of Gauss. Also, we deduce few inequalities for some partition functions.
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
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…
Leibniz's rule for the $n$-th derivative of a product is a very well known and extremely useful formula. In this article, we introduce an analogous explicit formula for the $n$-th derivative of a quotient of two functions. Later, we use…
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 propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions is extremely important. One of the reasons is that its error…
Let $r\geq 1$ be an integer, $\mathbf a=(a_1,\ldots,a_r)$ a vector of positive integers and let $D\geq 1$ be a common multiple of $a_1,\ldots,a_r$. In a continuation of a previous paper we prove that, if $D=1$ or $D$ is a prime number, the…
A close connection of reverse plane partitions with an integrable dynamical system called the discrete two-dimensional (2D) Toda molecule is clarified. It is shown that a multiplicative partition function for reverse plane partition of…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
In this note I revisit the calculation of partition function of simple one dimensional systems solvable by Bethe Ansatz. Particularly I show that by the precise definition and treatment of the partition function the nontrivial normalization…
In this paper, we derive some formulae involving coefficients of polynomials which occur quite naturally in the study of restricted partitions. Our method involves a recently discovered sieve technique by Li and Wan (Sci. China. Math.…
An approximate formula for the partitions of Goldbach's Conjecture is derived using Prime Number Theorem and a heuristic probabilistic approach. A strong form of Goldbach's conjecture follows in the form of a lower bounding function for the…
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function…
The explicit evaluation of the partition function in the Schwarzian theory is presented.
We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with…
The closed-form expression for the quantum partition function of the improved Tietz oscillator is obtained using the Voronoi summation formula.
In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The new method is benefited from a direct discretization approach and…