Enumeration of 3-regular one-face maps on orientable or non-orientable surface up to all symmetries
Abstract
We obtain explicit formulas for enumerating $3$-regular one-face maps on orientable and non-orientable surfaces of a given genus $g$ up to all symmetries. We use recent analytical results obtained by Bernardi and Chapuy for counting rooted precubic maps on non-orientable surfaces together with more widely known formulas for counting precubic maps on orientable surfaces. To take into account all symmetries we use a result of Krasko and Omelchenko that allows to reduce this problem to the problem of counting rooted quotient maps on orbifolds.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2019
- DOI:
- 10.48550/arXiv.1901.06591
- arXiv:
- arXiv:1901.06591
- Bibcode:
- 2019arXiv190106591K
- Keywords:
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- Mathematics - Combinatorics;
- 05C30
- E-Print:
- arXiv admin note: substantial text overlap with arXiv:1712.10139