2021/07/02 by Conley, Charles H., Ovsienko, Valentin
#05A15 (Primary) 05E16 #05A16 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.01234
We study a 2 × 2 matrix equation arising naturally in the theory of Coxeter frieze patterns. It is formulated in terms of the generators of the group PSL(2,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.