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arXiv · 1805.07530

Shabat Polynomials and Monodromy Groups of Trees Uniquely Determined by their Passport

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

A dessin d'enfant, or dessin, is a bicolored graph embedded into a Riemann surface. Acyclic dessins can be described analytically by pre-images of certain polynomials, called Shabat polynomials, and also algebraically by their monodromy groups, that is, the group generated by rotations of edges about black and white vertices. In this paper we investigate the Shabat polynomials and monodromy groups of planar acyclic dessins that are uniquely determined by their passports.

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Naiomi Cameron, Mary Kemp, Susan Maslak, Gabrielle Melamed, Richard A. Moy, Jonathan Pham, Austin Wei. 2018-05-19. Shabat Polynomials and Monodromy Groups of Trees Uniquely Determined by their Passport. https://doi.org/10.2140/involve.2019.12.791

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