Symbolic Integration and Special Functions [P20162-N18]

@inproceedings{RISC5478,
author = {Jose Capco and Georg Grasegger and Matteo Gallet and Christoph Koutschan and Niels Lubbes and Josef Schicho},
title = {{Computing the number of realizations of a Laman graph}},
booktitle = {{Electronic Notes in Discrete Mathematics (Proceedings of Eurocomb 2017)}},
language = {english},
abstract = {Laman graphs model planar frameworks which are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. In a recent paper we provide a recursion formula for this number of realizations using ideas from algebraic and tropical geometry. Here, we present a concise summary of this result focusing on the main ideas and the combinatorial point of view.},
volume = {61},
pages = {207--213},
isbn_issn = {ISSN 1571-0653},
year = {2017},
editor = {Vadim Lozin},
refereed = {yes},
keywords = {Laman graph; minimally rigid graph; tropical geometry; euclidean embedding; graph realization},
length = {7},
conferencename = {The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17)},
url = {http://www.koutschan.de/data/laman/}
}

@inproceedings{RISC5034,
author = {Shaoshi Chen and Manuel Kauers and Christoph Koutschan},
title = {{A Generalized Apagodu-Zeilberger Algorithm}},
booktitle = {{Proceedings of ISSAC 2014}},
language = {english},
pages = {107--114},
isbn_issn = {ISBN 978-1-4503-2501-1},
year = {2014},
editor = {Katsusuke Nabeshima},
refereed = {yes},
length = {8}
}

@inproceedings{RISC4512,
author = {Masao Ishikawa and Christoph Koutschan},
title = {{Zeilberger's Holonomic Ansatz for Pfaffians}},
booktitle = {{Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC)}},
language = {english},
abstract = {A variation of Zeilberger's holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger's approach is based on the Laplace expansion (cofactor expansion) of the determinant, we derive our approach from the cofactor expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper "Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary.},
pages = {227--233},
publisher = {ACM},
isbn_issn = {ISBN 978-1-4503-1269},
year = {2012},
editor = {Joris van der Hoeven and Mark van Hoeij},
refereed = {yes},
length = {7},
url = {http://www.risc.jku.at/people/ckoutsch/pfaffians/}
}

@inproceedings{RISC4513,
author = {Stavros Garoufalidis and Christoph Koutschan},
title = {{Twisting q-holonomic sequences by complex roots of unity}},
booktitle = {{Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC)}},
language = {english},
abstract = {A sequence f_n(q) is q-holonomic if it satisfies a nontrivial linear recurrence with coefficients polynomials in q and q^n. Our main theorems state that q-holonomicity is preserved under twisting, i.e., replacing q by w*q where w is a complex root of unity, and under the substitution q -> q^alpha where alpha is a rational number. Our proofs are constructive, work in the multivariate setting of \partial-finite sequences and are implemented in the Mathematica package HolonomicFunctions. Our results are illustrated by twisting natural q-holonomic sequences which appear in quantum topology, namely the colored Jones polynomial of pretzel knots and twist knots. The recurrence of the twisted colored Jones polynomial can be used to compute the asymptotics of the Kashaev invariant of a knot at an arbitrary complex root of unity.},
pages = {179--186},
publisher = {ACM},
isbn_issn = {ISBN 978-1-4503-1269},
year = {2012},
editor = {Joris van der Hoeven and Mark van Hoeij},
refereed = {yes},
length = {8},
url = {http://www.math.gatech.edu/~stavros/publications/twisting.qholonomic.data/}
}

@inproceedings{RISC3283,
author = {S. Beuchler and V. Pillwein and S. Zaglmayr},
title = {{Fast summation techniques for sparse shape functions in tetrahedral hp-FEM}},
booktitle = {{Domain Decomposition Methods in Science and Engineering XX}},
language = {english},
pages = {537--544},
isbn_issn = {?},
year = {2012},
note = {to appear},
editor = {?},
refereed = {yes},
length = {8}
}

@inproceedings{RISC4374,
author = {Viktor Levandovskyy and Christoph Koutschan and Oleksandr Motsak},
title = {{On Two-generated Non-commutative Algebras Subject to the Affine Relation}},
booktitle = {{Proceedings of CASC 2011}},
language = {english},
abstract = {We consider algebras over a field K, generated by two variables x and y subject to the single relation yx = qxy + ax + by + c for q in K^* and a, b, c in K. We prove, that among such algebras there are precisely five isomorphism classes. The representatives of these classes, which are ubiquitous operator algebras, are called model algebras. We derive explicit multiplication formulas for y^m x^n in terms of standard monomials x^i y^j for many algebras of the considered type. Such formulas are used in e.g. establishing formulas of binomial type and in an implementation of non-commutative multiplication in a computer algebra system. By using the formulas we also study centers and ring-theoretic properties of the non-commutative model algebras.},
series = {Lecture Notes in Computer Science},
volume = {6885},
pages = {309--320},
publisher = {Springer},
isbn_issn = {ISBN 978-3-642-23567-2},
year = {2011},
editor = {Vladimir Gerdt and Wolfram Koepf and Ernst W. Mayr and Evgenii Vorozhtsov},
refereed = {yes},
length = {12}
}

@inproceedings{RISC4375,
author = {Frederic Chyzak and James H. Davenport and Christoph Koutschan and Bruno Salvy},
title = {{On Kahan's Rules for Determining Branch Cuts}},
booktitle = {{Proceedings of the 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)}},
language = {english},
abstract = {In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.},
pages = {47--51},
publisher = {IEEE Computer Society: Conference Publishing Services (CPS)},
isbn_issn = {ISBN 978-0-7695-4630-8},
year = {2011},
editor = {Dongming Wang et al.},
refereed = {yes},
length = {5}
}