Related papers: An algorithm to classify the asymptotic set associ…
A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…
Let F=(F_1,...,F_n):C^n --> C^n be a polynomial mapping. By the multidegree of the mapping F we mean mdeg F=(deg F_1,...,deg F_n), an element of N^n. The aim of this paper is to study the following problem (especially for n=3): for which…
In this paper we study the asymptotics (as $n\to \infty$) of the sequences of Laguerre polynomials with varying complex parameters $\alpha$ depending on the degree $n$. More precisely, we assume that $\alpha_n = n A_n, $ and $ \lim_n A_n=A…
It is shown that the integral representation of Feynman diagrams in terms of the traditional Feynman parameters, when combined with properties of the Mellin--Barnes representation and the so called {\it converse mapping theorem}, provide a…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
Let $\mathbb{F}$ be a field of characteristic $p$, and let $UT_n(\mathbb{F})$ be the algebra of $n \times n$ upper triangular matrices over $\mathbb{F}$ with an involution of the first kind. In this paper we describe: the set of all…
The characterization of permutations over finite fields is an important topic in number theory with a long-standing history. This paper presents a systematic investigation of low-degree bivariate polynomial systems $F=(f_1(x,y),f_2(x,y))$…
In this paper, we propose a carefully optimized "half-gcd" algorithm for polynomials. We achieve a constant speed-up with respect to previous work for the asymptotic time complexity. We also discuss special optimizations that are possible…
We obtain new asymptotical bounds for the symmetric tensor rank of multiplication in any finite extension of any finite field $\F_q$. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on a family of Shimura…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
Asymptotic tensor rank is notoriously difficult to determine. Indeed, determining its value for the $2\times 2$ matrix multiplication tensor would determine the matrix multiplication exponent, a long-standing open problem. On the other…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We determine the asymptotic behavior of the coefficients of Hecke polynomials. In particular, this allows us to determine signs of these coefficients when the level or the weight is sufficiently large. In all but finitely many cases, this…
We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polynomials such that F is invertible if and only if the zero…
We study monic univariate polynomials whose coefficients are analytic functions of a real variable and whose roots lie in a specified analytic curve. These include characteristic polynomials of unitary and hermitian matrices whose entries…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach…
We consider the set of all graphs on n labeled vertices with prescribed degrees D=(d_1, ..., d_n). For a wide class of tame degree sequences D we prove a computationally efficient asymptotic formula approximating the number of graphs within…
Many combinatorial properties of a point set in the plane are determined by the set of possible partitions of the point set by a line. Their essential combinatorial properties are well captured by the axioms of oriented matroids. In fact,…