@article{1b632694e8d14267979f9fab2653352f,
title = "Catalog of dessins d'enfants with no more than 4 edges",
abstract = "In this work, all the dessins d'enfants with no more than 4 edges are listed and their Belyi pairs are computed. In order to enumerate all dessins, the technique of matrix model computations was used. The total number of dessins is 134; among them 77 are spherical, 53 of genus 1, and 4 of genus 2. The automorphism groups of all the dessins are also found. Dessins are listed by the number of edges. Dessins with the same number of edges are ordered lexicographically by their lists of 0-valencies. The corresponding matrix model for any list of 0-valencies is given and computed. Complex matrix models for dessins with 1-3 edges are used. For the dessins with 4 edges, we use Hermitian matrix model.",
author = "Adrianov, \{N. M.\} and Amburg, \{N. Ya\} and Dremov, \{V. A.\} and Kochetkov, \{Yu Yu\} and Kreines, \{E. M.\} and Levitskaya, \{Yu A.\} and Nasretdinova, \{V. F.\} and Shabat, \{G. B.\}",
note = "Funding Information: Acknowledgments. We would like to thank all participants of the scientific seminar “Graphs on surfaces and curves over number fields” for encouragement and interesting discussions. The 2nd, 5th, 7th, and 8th authors are grateful to the Russian Federal Nuclear Energy Agency for financial support. Also the 2nd author would like to acknowledge the grants NWO-RFBR 047.011.2004.026 (RFBR 05-02-89000-NWO-a), NSh-8004.2006.2, RFBR 07-01-00441-a, the 3rd, 5th, 6th, and 8th authors would like to acknowledge the grants RFBR 07-01-00441-a and NSh-5666.2006.1, the 5th author would like to acknowledge the grant MK-2687.2007.1, and the 7th author would like to acknowledge the grants RFBR 07-01-00441-a and NSh-8065.2006.2. The 5th author would like to express her deep gratitude to the Max Planck Institute of Mathematics in Bonn, where some part of this work was done, for the warm scientific atmosphere and financial support.",
year = "2009",
month = apr,
day = "1",
doi = "10.1007/s10958-009-9373-7",
language = "English",
volume = "158",
pages = "22--80",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer",
number = "1",
}