Vol. 12, No. 5, 2019

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Shabat polynomials and monodromy groups of trees uniquely determined by ramification type

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

Vol. 12 (2019), No. 5, 791–812
Abstract

A dessin d’enfant or dessin is a bicolored graph embedded into a Riemann surface. Acyclic dessins can be described analytically by preimages of Shabat polynomials and algebraically by their monodromy groups. We determine the Shabat polynomials and monodromy groups of planar acyclic dessins that are uniquely determined by their ramification types.

Keywords
dessins d'enfant, Shabat polynomials, monodromy groups, Belyi maps, trees, wreath products
Mathematical Subject Classification 2010
Primary: 11G32, 14H57
Secondary: 20E22
Milestones
Received: 2 May 2018
Revised: 3 November 2018
Accepted: 15 November 2018
Published: 22 May 2019

Communicated by Vadim Ponomarenko
Authors
Naiomi Cameron
Lewis & Clark College
Portland, OR
United States
Mary Kemp
Occidental College
Los Angeles, CA
United States
Susan Maslak
Ave Maria University
Ave Maria, FL
United States
Gabrielle Melamed
University of Hawaii at Manoa
Honolulu, HI
United States
Richard A. Moy
Lee University
Cleveland, TN
United States
Jonathan Pham
University of California
Irvine, CA
United States
Austin Wei
Pomona College
Claremont, CA
United States