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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 11G32, 14H57
Secondary: 20E22
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Milestones
Received: 2 May 2018
Revised: 3 November 2018
Accepted: 15 November 2018
Published: 22 May 2019
Communicated by Vadim Ponomarenko
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Authors |
| Naiomi Cameron | |
| Lewis & Clark College Portland, OR United States |
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| Mary Kemp | |
| Occidental College Los Angeles, CA United States |
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| Susan Maslak | |
| Ave Maria University Ave Maria, FL United States |
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| Gabrielle Melamed | |
| University of Hawaii at Manoa Honolulu, HI United States |
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| Richard A. Moy | |
| Lee University Cleveland, TN United States |
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| Jonathan Pham | |
| University of California Irvine, CA United States |
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| Austin Wei | |
| Pomona College Claremont, CA United States |
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