相关论文: Counting with rational generating functions
The main aim of this paper is twofold: (1) Suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions --- a way of writing an…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…
It is a common knowledge that the integer functions definable in simply typed lambda-calculus are exactly the extended polynomials. This is indeed the case when one interprets integers over the type (p->p)->p->p where p is a base type…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact formula and an asymptotic approximation. We also consider the…
Given a function $f$ in a finite field ${\mathbb F}_q$ of $q$ elements, we define the functional graph of $f$ as a directed graph on $q$ nodes labelled by the elements of ${\mathbb F}_q$ where there is an edge from $u$ to $v$ if and only if…
We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set of rational-valued functions, which generalize constraints.…
The paper proves sum-of-square-of-rational-function based representations (shortly, sosrf-based representations) of polynomial matrices that are positive semidefinite on some special sets: $\mathbb{R}^n;$ $\mathbb{R}$ and its intervals…
We extend to Barvinok's valuations the Euler-Maclaurin expansion formula which we obtained previously for the sum of values of a polynomial over the integral points of a rational polytope. This leads to an improvement of Barvinok's…
We prove that generating subspaces of matrix rings over finite fields are counted by polynomials. We use this result to define and study two-variable versions of polynomials counting isomorphism classes of absolutely irreducible…
We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of…
We introduce the notion of a scheduling problem which is a boolean function $S$ over atomic formulas of the form $x_i \leq x_j$. Considering the $x_i$ as jobs to be performed, an integer assignment satisfying $S$ schedules the jobs subject…
Alcoved polytopes are convex polytopes, which are the closure of a union of alcoves in an affine Coxeter arrangement. They are rational polytopes and, therefore, have Ehrhart quasipolynomials. Here we describe a method for computing the…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
We show that the generating function corresponding to the sequence of denominators of the best rational approximants of a quadratic irrational is a rational function with integer coefficients. Consequently we can compute the L\'evy constant…
Let the formal power series f in d variables with coefficients in an arbitrary field be a symmetric function decomposed as a series of Schur functions, and let f be a rational function whose denominator is a product of binomials of the form…
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed.…
The fact that Schubert polynomials are the weighted counting functions for reduced RC-graphs, also known as reduced pipe dreams, was established using their generating functions inside an appropriate Demazure algebra. Here we investigate…