Quiddities of polygon dissections and the Conway-Coxeter frieze equation

Autor:	Conley, Charles H., Ovsienko, Valentin
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics 05A15 (Primary) 05E16 05A16 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We study a $2 \times 2$ matrix equation arising naturally in the theory of Coxeter frieze patterns. It is formulated in terms of the generators of the group $\mathrm{PSL}(2,\mathbb{Z})$ and is closely related to continued fractions. It appears in a number of different areas, for example, toric varieties. We count its positive solutions, obtaining a series of integer sequences, some known and some new. This extends classical work of Conway and Coxeter proving that the first of these sequences is the Catalan numbers. Comment: 34 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2107.01234 Zobrazit plný text záznamu View this record from Arxiv