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arXiv · 1507.04414

Cylindrical Dyck paths and the Mazorchuk-Turowska equation

Jonas T. Hartwig·Daniele Rosso
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Abstract

We classify all solutions (p,q) to the equation p(u)q(u)=p(u+b)q(u+a) where p and q are complex polynomials in one indeterminate u, and a and b are fixed but arbitrary complex numbers. This equation is a special case of a system of equations which ensures that certain algebras defined by generators and relations are non-trivial. We first give a necessary condition for the existence of non-trivial solutions to the equation. Then, under this condition, we use combinatorics of generalized Dyck paths to describe all solutions and a canonical way to factor each solution into a product of irreducible solutions.

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Jonas T. Hartwig, Daniele Rosso. 2015-07-15. Cylindrical Dyck paths and the Mazorchuk-Turowska equation. https://doi.org/10.1007/s10801-016-0666-x

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