Rotundus: triangulations, Chebyshev polynomials, and Pfaffians
Combinatorics
2019-01-01 v1
Abstract
We introduce and study a cyclically invariant polynomial which is an analog of the classical tridiagonal determinant usually called the continuant. We prove that this polynomial can be calculated as the Pfaffian of a skew-symmetric matrix. We consider the corresponding Diophantine equation and prove an analog of a famous result due to Conway and Coxeter. We also observe that Chebyshev polynomials of the first kind arise as Pfaffians.
Cite
@article{arxiv.1707.09106,
title = {Rotundus: triangulations, Chebyshev polynomials, and Pfaffians},
author = {Charles Conley and Valentin Ovsienko},
journal= {arXiv preprint arXiv:1707.09106},
year = {2019}
}
Comments
8 pages