English

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.

Keywords

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

R2 v1 2026-06-22T20:59:47.103Z