4 citations · 5 across the 6 of their papers we have counts for
9 papers
Separated Variables on Plane Algebraic Curves
Manfred Buchacher
We investigate the problem of deciding whether the restriction of a rational function to the curve associated with an irreducible polynomial $p\in\mathbb{K}[x…
On the Problem of Separating Variables in Multivariate Polynomial Ideals
Manfred Buchacher, Manuel Kauers
For a given ideal I in K[x_1,...,x_n,y_1,...,y_m] in a polynomial ring with n+m variables, we want to find all elements that can be written as f-g for some f in K[x_1,...,x_n] and…
Separating Variables in Bivariate Polynomial Ideals: the Local Case
Manfred Buchacher
We present a semi-algorithm which for any irreducible finds all elements of that are of the form for some $q\in\mathbb{K}…
The Orbit-Sum Method for Higher Order Equations
Manfred Buchacher, Manuel Kauers
The orbit-sum method is an algebraic version of the reflection-principle that was introduced by Bousquet-Mélou and Mishna to solve functional equations that arise in the enumeratio…
The Newton-Puiseux algorithm and effective algebraic series
Manfred Buchacher
We explain how to encode an algebraic series by finite data and how to do effective arithmetic on the level of these encodings. The reasoning is based on the Newton-Puiseux algorit…
Quadrant Walks Starting Outside the Quadrant
Manfred Buchacher, Manuel Kauers, Amelie Trotignon
We investigate a functional equation which resembles the functional equation for the generating function of a lattice walk model for the quarter plane. The interesting feature of t…
Walks with Small Steps in the 4D-Orthant
Manfred Buchacher, Sophie Hofmanninger, Manuel Kauers
We provide some first experimental data about generating functions of restricted lattice walks with small steps in NN^4.
Separating Variables in Bivariate Polynomial Ideals
Manfred Buchacher, Manuel Kauers, Gleb Pogudin
We present an algorithm which for any given ideal finds all elements of that have the form , i.e., all elements in which no monomial i…
Inhomogeneous Restricted Lattice Walks
Manfred Buchacher, Manuel Kauers
We consider inhomogeneous lattice walk models in a half-space and in the quarter plane. For the models in a half-space, we show by a generalization of the kernel method to linear s…