Abstract. In this paper a concise but systematic account of the relations between Shabat polynomials and plane trees is given, including the famous equivalence theorem for plane trees attributed to Riemann--Belyi--Grothendieck--Shabat. Furthermore, some analytical features of Shabat polynomials and metric properties of Shabat trees are discussed.
AMS Subject Classification
(1991): 05C05, 05C10, 30C10, 30C85, 30F99
Received November 11, 2017 and in final form February 7, 2018. (Registered under 71/2017.)