Related papers: Generating linear categories of partitions

Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate…

We propose new algorithms for the computation of the first N terms of a vector (resp. a basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations which is…

Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…

We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…

Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…

The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…

In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables…

This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann…

We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…

We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of abstract polymer models formalism of Koteck\'y and Preiss. We apply our framework…

For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…

Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…

We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…

We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so…

A simple algorithm with quasi-linear time complexity and linear space complexity for the evaluation of the hypergeometric series with rational coefficients is constructed. It is shown that this algorithm is suitable in practical informatics…

Set partitions closed under certain operations form a tensor category. They give rise to certain subgroups of the free orthogonal quantum group $O_n^+$, the so called easy quantum groups, introduced by Banica and Speicher in 2009. This…

In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…

This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…

The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…