Christoph Koutschan
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Christoph Koutschan has a total of 112 co-authors. Here are the top co-authors by number of shared publications:
- Stavros Garoufalidis
Southern University of Science and Technology, Shenzhen, P. R. China
7 shared publications - Jean-Marie Maillard
LPTMC The University of Melbourne 3010 Vic Australia
6 shared publications Manuel Kauers
6 shared publicationsJosef Schicho
RISC, Johannes Kepler University,Linz,Austria
4 shared publications- Manuel Kauers
Institute for Algebra, Johannes Kepler University, Linz, Austria
4 shared publications Shaoshi Chen
4 shared publications
Latest Publications
- 1 January 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 72 (9) , 1
Representing Piecewise-Linear Functions by Functions with Minimal Arity
- 1 January 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 72 (9) , 1
Representing Piecewise-Linear Functions by Functions with Minimal Arity
- Open Access
- 28 July 2025
- Published by Association for Computing Machinery (ACM)
- p. 70-78
Non-minimality of minimal telescopers explained by residues
- 28 July 2025
- Published by Association for Computing Machinery (ACM)
- p. 70-78
Open AccessNon-minimality of minimal telescopers explained by residues
- Open Access
- 11 June 2025
- Published by Elsevier in Journal of Symbolic Computation
- Vol. 132
How to generate all possible rational Wilf–Zeilberger forms?
- 11 June 2025
- Published by Elsevier in Journal of Symbolic Computation
- Vol. 132
Open AccessHow to generate all possible rational Wilf–Zeilberger forms?
- 3 July 2024
- Published by Elsevier in Journal of Symbolic Computation
- Vol. 127
Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations
- 3 July 2024
- Published by Elsevier in Journal of Symbolic Computation
- Vol. 127
Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations
- 26 September 2023
- Published by Springer Nature in Applicable Algebra in Engineering, Communication and Computing
- Vol. 36 (4) , 595-610
Representing piecewise linear functions by functions with small arity
- 26 September 2023
- Published by Springer Nature in Applicable Algebra in Engineering, Communication and Computing
- Vol. 36 (4) , 595-610
Representing piecewise linear functions by functions with small arity
- Open Access
Diagonally symmetric alternating sign matrices
The enumeration of diagonally symmetric alternating sign matrices (DSASMs) is studied, and a Pfaffian formula is obtained for the number of DSASMs of any fixed size, where the entries for the Pfaffian are positive integers given by simple binomial coefficient expressions. This result provides the first known case of an exact enumeration formula for an alternating sign matrix symmetry class in which a simple product formula does not seem to exist. Pfaffian formulae are also obtained for DSASM generating functions associated with several natural statistics, including the number of nonzero strictly upper triangular entries in a DSASM, the number of nonzero diagonal entries in a DSASM, and the column of the unique 1 in the first row of a DSASM. The proofs of these results involve introducing a version of the six-vertex model whose configurations are in bijection with DSASMs of fixed size, and obtaining a Pfaffian expression for its partition function. Various further results and conjectures are also obtained, including some related to the exact enumeration of off-diagonally symmetric alternating sign matrices, and some related to the asymptotic enumeration of DSASMs and other classes of alternating sign matrices.
Open AccessDiagonally symmetric alternating sign matrices
The enumeration of diagonally symmetric alternating sign matrices (DSASMs) is studied, and a Pfaffian formula is obtained for the number of DSASMs of any fixed size, where the entries for the Pfaffian are positive integers given by simple binomial coefficient expressions. This result provides the first known case of an exact enumeration formula for an alternating sign matrix symmetry class in which a simple product formula does not seem to exist. Pfaffian formulae are also obtained for DSASM generating functions associated with several natural statistics, including the number of nonzero strictly upper triangular entries in a DSASM, the number of nonzero diagonal entries in a DSASM, and the column of the unique 1 in the first row of a DSASM. The proofs of these results involve introducing a version of the six-vertex model whose configurations are in bijection with DSASMs of fixed size, and obtaining a Pfaffian expression for its partition function. Various further results and conjectures are also obtained, including some related to the exact enumeration of off-diagonally symmetric alternating sign matrices, and some related to the asymptotic enumeration of DSASMs and other classes of alternating sign matrices.
- Open Access
- 24 July 2023
- Published by Association for Computing Machinery (ACM)
- p. 434-442
A Unified Approach to Unimodality of Gaussian Polynomials
In 2013, Pak and Panova proved the strict unimodality property of q-binomial coefficients (as polynomials in q) based on the combinatorics of Young tableaux and the semigroup property of Kronecker coefficients. They showed it to be true for all ℓ, m ≥ 8 and a few other cases. We propose a different approach to this problem based on computer algebra, where we establish a closed form for the coefficients of these polynomials and then use cylindrical algebraic decomposition to identify exactly the range of coefficients where strict unimodality holds. This strategy allows us to tackle generalizations of the problem, e.g., to show unimodality with larger gaps or unimodality of related sequences. In particular, we present proofs of two additional cases of a conjecture by Stanley and Zanello.
- 24 July 2023
- Published by Association for Computing Machinery (ACM)
- p. 434-442
Open AccessA Unified Approach to Unimodality of Gaussian Polynomials
In 2013, Pak and Panova proved the strict unimodality property of q-binomial coefficients (as polynomials in q) based on the combinatorics of Young tableaux and the semigroup property of Kronecker coefficients. They showed it to be true for all ℓ, m ≥ 8 and a few other cases. We propose a different approach to this problem based on computer algebra, where we establish a closed form for the coefficients of these polynomials and then use cylindrical algebraic decomposition to identify exactly the range of coefficients where strict unimodality holds. This strategy allows us to tackle generalizations of the problem, e.g., to show unimodality with larger gaps or unimodality of related sequences. In particular, we present proofs of two additional cases of a conjecture by Stanley and Zanello.
- Open Access
- 24 July 2023
- Published by Association for Computing Machinery (ACM)
- p. 372-380
Transcendence Certificates for D-finite Functions
Although in theory we can decide whether a given D-finite function is transcendental, transcendence proofs remain a challenge in practice. Typically, transcendence is certified by checking certain incomplete sufficient conditions. In this paper we propose an additional such condition which catches some cases on which other tests fail.
- 24 July 2023
- Published by Association for Computing Machinery (ACM)
- p. 372-380
Open AccessTranscendence Certificates for D-finite Functions
Although in theory we can decide whether a given D-finite function is transcendental, transcendence proofs remain a challenge in practice. Typically, transcendence is certified by checking certain incomplete sufficient conditions. In this paper we propose an additional such condition which catches some cases on which other tests fail.
- Open Access
On Potentials Integrated by the Nikiforov-Uvarov Method
We discuss basic potentials of the nonrelativistic and relativistic quantum mechanics that can be integrated in the Nikiforov and Uvarov paradigm with the aid of a computer algebra system. This consideration may help the readers to study analytical methods of quantum physics.
Open AccessOn Potentials Integrated by the Nikiforov-Uvarov Method
We discuss basic potentials of the nonrelativistic and relativistic quantum mechanics that can be integrated in the Nikiforov and Uvarov paradigm with the aid of a computer algebra system. This consideration may help the readers to study analytical methods of quantum physics.
- Open Access
Diagonals of Rational Functions: From Differential Algebra to Effective Algebraic Geometry
We show that the results we had previously obtained on diagonals of 9- and 10-parameter families of rational functions in three variables , , and , using creative telescoping, yielding modular forms expressed as pullbacked hypergeometric functions, can be obtained much more efficiently by calculating the -invariant of an elliptic curve canonically associated with the denominator of the rational functions. These results can be drastically generalized by changing the parameters into arbitrary rational functions of the product . In other cases where creative telescoping yields pullbacked hypergeometric functions, we extend this algebraic geometry approach to other families of rational functions in three or more variables. In particular, we generalize this approach to rational functions in more than three variables when the denominator can be associated to an algebraic variety corresponding to products of elliptic curves, or foliations in elliptic curves. We also extend this approach to rational functions in three variables when the denominator is associated with a genus-two curve such that its Jacobian is a split Jacobian, corresponding to the product of two elliptic curves. We sketch the situation where the denominator of the rational function is associated with algebraic varieties that are not of the general type, having an infinite set of birational automorphisms. We finally provide some examples of rational functions in more than three variables, where the telescopers have pullbacked hypergeometric solutions, because the denominator corresponds to an algebraic variety that has a selected elliptic curve.Open AccessDiagonals of Rational Functions: From Differential Algebra to Effective Algebraic Geometry
We show that the results we had previously obtained on diagonals of 9- and 10-parameter families of rational functions in three variables , , and , using creative telescoping, yielding modular forms expressed as pullbacked hypergeometric functions, can be obtained much more efficiently by calculating the -invariant of an elliptic curve canonically associated with the denominator of the rational functions. These results can be drastically generalized by changing the parameters into arbitrary rational functions of the product . In other cases where creative telescoping yields pullbacked hypergeometric functions, we extend this algebraic geometry approach to other families of rational functions in three or more variables. In particular, we generalize this approach to rational functions in more than three variables when the denominator can be associated to an algebraic variety corresponding to products of elliptic curves, or foliations in elliptic curves. We also extend this approach to rational functions in three variables when the denominator is associated with a genus-two curve such that its Jacobian is a split Jacobian, corresponding to the product of two elliptic curves. We sketch the situation where the denominator of the rational function is associated with algebraic varieties that are not of the general type, having an infinite set of birational automorphisms. We finally provide some examples of rational functions in more than three variables, where the telescopers have pullbacked hypergeometric solutions, because the denominator corresponds to an algebraic variety that has a selected elliptic curve.