• Corpus ID: 227247582

The generating function of Kreweras walks with interacting boundaries is not algebraic.

@article{Bostan2020TheGF,
  title={The generating function of Kreweras walks with interacting boundaries is not algebraic.},
  author={Alin Bostan and Manuel Kauers and Thibaut Verron},
  journal={arXiv: Combinatorics},
  year={2020}
}
Beaton, Owczarek and Xu (2019) studied generating functions of Kreweras walks and of reverse Kreweras walks in the quarter plane, with interacting boundaries. They proved that for the reverse Kreweras step set, the generating function is always algebraic, and for the Kreweras step set, the generating function is always D-finite. However, apart from the particular case where the interactions are symmetric in $x$ and~$y$, they left open the question of whether the latter one is algebraic. Using… 
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References

SHOWING 1-10 OF 19 REFERENCES
Quarter-Plane Lattice Paths with Interacting Boundaries: The Kreweras and Reverse Kreweras Models
Lattice paths in the quarter plane have led to a large and varied set of results in recent years. One major project has been the classification of step sets according to the properties of the
Exact Solution of Some Quarter Plane Walks with Interacting Boundaries
TLDR
This work investigates how integrability may change in those 23 models where in addition to length one also counts the number of sites of the walk touching either the horizontal and/or vertical boundaries of the quarter plane.
The complete Generating Function for Gessel Walks is Algebraic
TLDR
It is proved that if $g(n;i,j)$ denotes the number of Gessel walks of length $n$ which end at the point $( i,j)\in\set N^2$, then the trivariate generating series $G(t;x,y)x^i y^j t^n$ is an algebraic function.
Advanced applications of the holonomic systems approach
TLDR
This thesis contributed to translating Takayama's algorithm into a new context, in order to apply it to an until then open problem, the proof of Ira Gessel's lattice path conjecture, and to make the underlying computations feasible the authors employed a new approach for finding creative telescoping operators.
Analytic Models and Ambiguity of Context-Free Languages
Differentiably Finite Power Series
A Fast Approach to Creative Telescoping
TLDR
This note reinvestigate the task of computing creative telescoping relations in differential–difference operator algebras using an ansatz that explicitly includes the denominators of the delta parts and shows that it can be superior to existing methods by a large factor.
Rational Solutions of the Mixed Differential Equation and Its Application to Factorization of Differential Operators
TLDR
A fast method to compute the rational solutions of a certain differential equation that will be called the mixed differential equation can be applied to speed up the factorization of completely reducible linear differential operators with rational functions coefficients.
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