A292971
Number of 4-regular maps with n vertices on the torus, up to orientation-preserving isomorphisms.
Original entry on oeis.org
1, 4, 23, 185, 1647, 16455, 169734, 1805028, 19472757, 212603589, 2341275180, 25969695728, 289782412836, 3250137255678
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv preprint arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
A292972
Number of 5-regular maps with 2n vertices on the torus, up to orientation-preserving isomorphisms.
Original entry on oeis.org
15, 6423, 4031952, 2839677570, 2111005408320, 1624203259187196, 1280171373413389056, 1027235174396893007472, 835745211680299639976976, 687471000510964612782875472
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv preprint arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
A292468
Number of 4-regular maps with n vertices on the torus, up to orientation-preserving and orientation-reversing isomorphisms.
Original entry on oeis.org
1, 4, 20, 133, 1013, 9209, 89889, 929373, 9880120, 107087360, 1174950951, 13008800489, 145024885270, 1625819872988, 18311555574347, 207068032188985, 2349706730746994, 26745505016101977, 305267158873891108, 3492857897924201864
Offset: 1
- E. Krasko and A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part II: Enumeration of Unsensed Maps, arXiv preprint arXiv:1709.03230 [math.CO], 2017. See Table 1, p. 20.
- E. Krasko and A. Omelchenko, Enumeration of r-regular maps on the torus. Part II: Unsensed maps, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 600-614.
A292974
Number of 6-regular maps with n vertices on the torus, up to orientation-preserving isomorphisms.
Original entry on oeis.org
3, 81, 3313, 171282, 9444158, 541659909, 31819176850, 1902508129720, 115307287484560, 7064528615347192, 436658221692698200, 27188662712300575980, 1703444238720524912060
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv preprint arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
A112948
Number of unrooted 3-regular planar maps with 2n vertices, up to orientation-preserving isomorphisms.
Original entry on oeis.org
2, 6, 26, 191, 1904, 22078, 282388, 3848001, 54953996, 814302292
Offset: 1
There exist 2 planar maps with two 3-valent vertices: a map with three parallel edges and a map with one loop in each vertex and a link connecting the vertices. Therefore a(1)=2.
- Z. C. Gao, V. A. Liskovets and N. C. Wormald, Enumeration of unrooted odd-valent regular planar maps, Preprint, 2005.
- Mark van Hoeij, Vijay Jung Kunwar, Classifying (near)-Belyi maps with Five Exceptional Points, arXiv preprint arXiv:1604.08158, 2016. Also in Indagationes Mathematicae (2019) Vol. 30, No. 1, 136-156.
- Riccardo Murri, Fatgraph algorithms and the homology of the Kontsevich complex, arXiv preprint arXiv:1202.1820, 2012.
3-regular maps on the torus:
A292408.
A292110
Number of 6-regular maps with n vertices on the torus, up to orientation-preserving and orientation-reversing isomorphisms.
Original entry on oeis.org
3, 61, 1936, 89986, 4791784, 272005507, 15929826713, 951610091294, 57659992554993, 3532378891197016, 218331197907776846, 13594369669588615612
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part II: Enumeration of Unsensed Maps, arXiv preprint arXiv:1709.03230 [math.CO], 2017. See Table 1, p. 20.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part II: Unsensed maps, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 600-614.
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