Free subgroups of free products and combinatorial hypermaps
| Autor: | Laura Ciobanu, Alexander Kolpakov |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Group Theory (math.GR)
0102 computer and information sciences 01 natural sciences Subgroup growth Theoretical Computer Science Combinatorics Mathematics - Geometric Topology Mathematics::Group Theory Conjugacy class FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics 0101 mathematics Mathematics Recurrence relation 010102 general mathematics Dessin d'enfant Geometric Topology (math.GT) 16. Peace & justice Connection (mathematics) Free product 010201 computation theory & mathematics Free group 14N10 20E07 20H10 05E45 33C20 Combinatorics (math.CO) Isomorphism Mathematics - Group Theory |
| Zdroj: | Discrete Mathematics. 342:1415-1433 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2019.01.014 |
| Popis: | We derive a generating series for the number of free subgroups of finite index in $\Delta^+ = \mathbb{Z}_p*\mathbb{Z}_q$ by using a connection between free subgroups of $\Delta^+$ and certain hypermaps (also known as ribbon graphs or "fat" graphs), and show that this generating series is transcendental. We provide non-linear recurrence relations for the above numbers based on differential equations that are part of the Riccati hierarchy. We also study the generating series for conjugacy classes of free subgroups of finite index in $\Delta^+$, which correspond to isomorphism classes of hypermaps. Asymptotic formulas are provided for the numbers of free subgroups of given finite index, conjugacy classes of such subgroups, or, equivalently, various types of hypermaps and their isomorphism classes. Comment: 27 pages, 3 figures; supplementary SAGE worksheets available at http://sashakolpakov.wordpress.com/list-of-papers/ |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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