相关论文: On Explicit Formula for Restricted Partition Funct…
The 2-adic valuation of an integer n which is the exponent of the highest power of 2 that divides n. In this paper, we give representations of certain restricted partition functions in terms of 2-adic valuation.
A vector partition function is the number of ways to write a vector as a non-negative integer-coefficient sum of the elements of a finite set of vectors $\Delta$. We present a new algorithm for computing closed-form formulas for vector…
We give an elementary algebraic proof of Paradan's wall crossing formulae for partition functions. We also express such jumps in volume and partition functions by one dimensional residue formulae. Subsequently we reprove the relation…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often…
Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment…
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.…
Partition of unities appear in many places in analysis. Typically they are generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire…
The number partition problem is a well-known problem, which is one of 21 Karp's NP-complete problems \cite{karp}. The partition function is a boolean function that is equivalent to the number partition problem with number range restricted.…
Explicit expressions for restricted partition function $W(s,{\bf d}^m)$ and its quasiperiodic components $W_j(s,{\bf d}^m)$ (called {\em Sylvester waves}) for a set of positive integers ${\bf d}^m = \{d_1, d_2, ..., d_m\}$ are derived. The…
We describe how the Hardy-Ramanujan-Rademacher formula can be implemented to allow the partition function $p(n)$ to be computed with softly optimal complexity $O(n^{1/2+o(1)})$ and very little overhead. A new implementation based on these…
In this note we consider several kind of partition functions of one-dimensional models with nearest - neighbor interactions $I_n, n\in \mathbf{Z}$ and spin values $\pm 1$. We derive systems of recursive equations for each kind of such…
Given a Fractional Repetition code, finding the reconstruction and repair degree in a distributed storage system is an important problem. In this work, we present algorithms for computing the reconstruction and repair degree of fractional…
The most essential problems in Regge calculus discretization are the definitions of the partition function and the integral measure for link--length. In recent work, by considering the one--dimensional case, it was suggested that we should…
We introduce the difference operator for functions defined on strict partitions and prove a polynomiality property for a summation involving the hook length and content statistics. As an application, several new hook-content formulas for…
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive semi-definite Hamiltonians, our method has expected running-time that is almost linear in $(M/(\epsilon_{\rm…
Suppose that $a_1(n),a_2(n),...,a_s(n),m(n)$ are integer-valued polynomials in $n$ with positive leading coefficients. This paper presents Popoviciu type formulas for the generalized restricted partition function…
We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…
The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit representations of these functions. Taking advantage of their…
The partition function $p(n)$ has been a testing ground for applications of analytic number theory to combinatorics. In particular, Hardy and Ramanujan invented the "circle method" to estimate the size of $p(n)$, which was later perfected…