Domino tilings and products of Fibonacci and Pell numbers.
In this article, we study the complexity of drunken man infinite words. We show that these infinite words, generated by a deterministic and complete countable automaton, or equivalently generated by a substitution over a countable alphabet of constant length, have complexity functions equivalent to n(log2n)2 when n goes to infinity.
It is shown that duality triads of higher rank are closely related to orthogonal matrix polynomials on the real line. Furthermore, some examples of duality triads of higher rank are discussed. In particular, it is shown that the generalized Stirling numbers of rank r give rise to a duality triad of rank r.