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We present a general method to obtain asymptotic power series for three kinds of sequences. And we give recurrence relations for determining the coefficients of asymptotic power series for these sequences. As applications, we show how these…
Given the first 20-100 coefficients of a typical generating function of the type that arises in many problems of statistical mechanics or enumerative combinatorics, we show that the method of differential approximants performs surprisingly…
This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers,…
We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated…
We pursue the investigation of generalizations of the Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word. The finite…
We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from a single trajectory of noisy observations. Identifying unknown differential equations from noisy…
We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…
We compute the asymptotic number of monic trace-one integral polynomials with Galois group $C_3$ and bounded height. For such polynomials we compute a height function coming from toric geometry and introduce a parametrization using the…
Integration operational matrix methods based on Zernike polynomials are used to determine approximate solutions of a class of non-homogeneous partial differential equations (PDEs) of first and second order. Due to the nature of the Zernike…
Odlyzko and Stanley introduced a greedy algorithm for constructing infinite sequences with no 3-term arithmetic progressions when beginning with a finite set with no 3-term arithmetic progressions. The sequences constructed from this…
We use connection relations and series rearrangement to generalize generating functions for several higher continuous orthogonal polynomials in the Askey scheme, namely the Wilson, continuous dual Hahn, continuous Hahn, and…
The computation of Kronecker coefficients is a challenging problem with a variety of applications. In this paper we present an approach based on methods from symplectic geometry and residue calculus. We outline a general algorithm for the…
Estimating the number of triangles in a graph is one of the most fundamental problems in sublinear algorithms. In this work, we provide an algorithm that approximately counts the number of triangles in a graph using only polylogarithmic…
Canonical orderings [STOC'88, FOCS'92] have been used as a key tool in graph drawing, graph encoding and visibility representations for the last decades. We study a far-reaching generalization of canonical orderings to non-planar graphs…
The polynomials that arise as coefficients when a power series is raised to the power $x$ include many important special cases, which have surprising properties that are not widely known. This paper explains how to recognize and use such…
We develop a new algorithm to compute determinants of all possible Hankel matrices made up from a given finite length sequence over a finite field. Our algorithm fits within the dynamic programming paradigm by exploiting new recursive…
The research aims to construct a new type of matrix called the Fibonacci-Hessenberg-Lorentz matrix by multiplying Fibonacci-Hessenberg matrices with Lorentz matrix multiplication. The study will start by examining the properties of…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
There has been considerable recent literature connecting Poncelet's theorem to ellipses, Blaschke products and numerical ranges, summarized, for example, in the recent book [11]. We show how those results can be understood using ideas from…
We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a…