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Cameron, Naiomi; Kemp, Mary; Maslak, Susan; Melamed, Gabrielle; Moy, Richard A.; Pham, Jonathan; Wei, Austin

Shabat polynomials and monodromy groups of trees uniquely determined by ramification type. (English) Zbl 1452.11073

Involve 12, No. 5, 791-812 (2019).
A tree is a graph without any loops. A plane tree is a tree with an embedding into the plane or equivalently a tree together with an ordering of edges emanating from vertices. A map of plane trees preserving this extra structure is called an isomorphism of plane trees. Enumeration problem of isomorphism classes of plane trees as well as their complete list (in terms of their ramification types) is addressed in [G. Shabat and A. Zvonkin, Contemp. Math. 178, 233–275 (1994; Zbl 0816.05024)].
Building on this, the authors determine the corresponding Belyi maps (called Shabat polynomials) and their monodromy groups.
Reviewer: Ayberk Zeytin (Istanbul)

MSC:

11G32 Arithmetic aspects of dessins d’enfants, Belyĭ theory
14H57 Dessins d’enfants theory
20E22 Extensions, wreath products, and other compositions of groups

Keywords:

dessin d’enfant; Shabat polynomials; monodromy groups; Belyi maps; plane trees

Citations:

Zbl 0816.05024
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\textit{N. Cameron} et al., Involve 12, No. 5, 791--812 (2019; Zbl 1452.11073)
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