Integrability properties of Motzkin polynomials

@article{Gahramanov2017IntegrabilityPO,
  title={Integrability properties of Motzkin polynomials},
  author={Ilmar Gahramanov and Edvard T. Musaev},
  journal={arXiv: High Energy Physics - Theory},
  year={2017}
}
We consider a Hamiltonian system which has its origin in a generalization of exact renormalization group flow of matrix scalar field theory and describes a non-linear generalization of the shock-wave equation that is known to be integrable. Analyzing conserved currents of the system the letter shows, that these follow a nice pattern governed by coefficients of Motzkin polynomials, where each integral of motion corresponds to a path on a unit lattice. 

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