A292974 -id:A292974 - cp's OEIS frontend

A292408 Number of 3-regular maps with 2n vertices on the torus, up to orientation-preserving isomorphisms.

1, 5, 46, 669, 11096, 196888, 3596104, 66867564, 1258801076, 23925376862, 458284630844, 8835496339452, 171286387714900, 3336406717216564, 65257828878990784, 1281049596756607960, 25228921286295314736, 498287389997552607290, 9866927329534881618772, 195837489338961245840240

Offset: 1

Evgeniy Krasko, Sep 15 2017

nonn

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.
Riccardo Murri, Fatgraph algorithms and the homology of the Kontsevich complex, arXiv preprint arXiv:1202.1820, 2012.

3-regular maps on the sphere: A112948.

Cf. A292971 (4-regular), A292972 (5-regular), A292974 (6-regular).

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

Evgeniy Krasko, Sep 27 2017

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.

Cf. A292408 (3-regular), A292972 (5-regular), A292974 (6-regular).

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

Evgeniy Krasko, Sep 27 2017

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.

Cf. A292408 (3-regular), A292971 (4-regular), A292974 (6-regular).

cp's OEIS Frontend

A292408 Number of 3-regular maps with 2n vertices on the torus, up to orientation-preserving isomorphisms.

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A292971 Number of 4-regular maps with n vertices on the torus, up to orientation-preserving isomorphisms.

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A292972 Number of 5-regular maps with 2n vertices on the torus, up to orientation-preserving isomorphisms.

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