Operations on the set of scalar and matrix-valued quiddity sequences

Abstract

Our purpose with this paper is, in first place, to recast the space of quiddity sequences corresponding to usual frieze patterns as a different type of SET operad, and second to introduce and study $\mathfrak{M}$-quiddity sequences where $\mathfrak{M}$ is a monodromy block matrix of order two. Also, we examine some related topic as are the possibility of to define matrix-valued friezes patterns and noncommutative signed Chebyshev polynomials.