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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 problem and then illustrate its effectiveness in several interesting examples. Significantly, our algorithm does not only compute individual Kronecker coefficients, but also symbolic formulas that are valid on an entire polyhedral chamber. As a byproduct, we are able to compute several Hilbert series. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method for computing bounded-degree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in lacunary representation and a degree bound d and computes the irreducible factors of degree at most d of f in time polynomial in the lacunary size of f and in d . Our algorithm, which is valid for any field of zero characteristic, is based on a new gap theorem that enables reducing the problem to several instances of (a) the univariate case and (b) low-degree multivariate factorization. The reduction algorithms we propose are elementary in that they only manipulate the exponent vectors of the input polynomial. The proof of correctness and the complexity bounds rely on the Newton polytope of the polynomial, where the underlying valued field consists of Puiseux series in a single variable. [ABSTRACT FROM AUTHOR]

This paper describes the fastest quantum algorithm at this moment for the quantum Fourier transform (QFT) over symmetric groups. We provide a new FFT (classical) algorithm over symmetric groups and then transform it to a quantum algorithm. The complexity of our QFT algorithm is O ( n 3 log ⁡ n ) , faster than the existing O ( n 4 log ⁡ n ) QFT algorithm. In addition, we show that the algorithm can be performed in O ( n 3 ) if the use of threshold gates is allowed. [ABSTRACT FROM AUTHOR]

The main goal of the paper is to present an algorithm to realize the theoretical method by Berlyand and Mityushev (2001, 2005) for computations of the effective conductivity of fibrous composites expressed in therms of the linear combinations of the basic e -sums. Algorithms are presented in Mathematical Pseudo-language with examples in Mathematica ® . A method for simplifying the basic e -sums by reducing mirror terms is presented. Developed algorithms are applied to the optimal packing problem of disks in the plane. [ABSTRACT FROM AUTHOR]