Related papers: Decomposing replicable functions
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial,…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
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…
In this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombination strategy is the used of Darboux polynomials. We study…
In product design, a decomposition of the overall product function into a set of smaller, interacting functions is usually considered a crucial first step for any computer-supported design tool. Here, we propose a new approach for the…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…
We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified.…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
We define two recursive functions obtained by decomposition of a given interval into four close parts and prove two lemmas which determine features of these functions.
An algorithm is designed which decomposes a tropical univariate rational function into a composition of tropical binomials and trinomials. When a function is monotone, the composition consists just of binomials. Similar algorithms are…
We present an algorithm that determines the Galois group of linear difference equations with rational function coefficients.
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
A finitely generated group admits a decomposition, called its Grushko decomposition, into a free product of freely indecomposable groups. There is an algorithm to construct the Grushko decomposition of a finite graph of finite rank free…
The partial success of the block renormalization group techniques is analysed in terms of a functional operator which formalizes the idea of self-replicability of a system in terms of smaller blocks which are similar to the original. The…
Submodular functions are at the core of many machine learning and data mining tasks. The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. In many data…
We present a new method for the reconstruction of rational functions through finite-fields sampling that can significantly reduce the number of samples required. The method works by exploiting all the independent linear relations among…
We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the…