Related papers: MacMahon's $\Omega_\geq$ operator: A computational…
We describe a unified approach to calculating the partition functions of a general multi-level system with a free Hamiltonian. Particularly, we present new results for parastatistical systems of any order in the second quantized approach.…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
We present two algorithms, one quantum and one classical, for estimating partition functions of quantum spin Hamiltonians. The former is a DQC1 (Deterministic quantum computation with one clean qubit) algorithm, and the first such for…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
Recently, Andrews and Paule studied Schmidt type partitions using MacMahon's Partition Analysis and obtained various interesting results. In this paper, we focus on the combinatorics of Schmidt type partition theorems and characterize them…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
In the present work, we extend current research in a nearly-forgotten but newly revived topic, initiated by P. A. MacMahon, on a generalized notion which relates the divisor sums to the theory of integer partitions and two infinite families…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
Combining principles with pragmatism, a new approach and accompanying algorithm are presented to a longstanding problem in applied statistics: the interpretation of principal components. Following Rousson and Gasser [53 (2004) 539--555]…
We use sums over integer compositions analogous to generating functions in partition theory, to express certain partition enumeration functions as sums over compositions into parts that are $k$-gonal numbers; our proofs employ Ramanujan's…
Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion…
In this paper we revisit the work of E.T. Bell concerning partition polynomials in order to introduce the reciprocal partition polynomials. We give their explicit formulas and apply the result to compute closed formulae for some well-known…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
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 this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ram\'irez C., Math. Program. 104 (2005), no. 2-3, Ser. B,…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
Various problems of mathematical physics consider octonions and split-octonions as a mathematical structure, which underpins the eight-dimensional nature of these problems. Therefore, it is not surprising that octonionic analysis has become…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
The tetrahedron equation introduced by Zamolodchikov is a three-dimensional generalization of the Yang-Baxter equation. Several types of solutions to the tetrahedron equation that have connections to quantum groups can be viewed as…