A268571 -id:A268571 - cp's OEIS frontend

Showing 1-4 of 4 results.

A268568 Number of immersions of oriented circle into oriented sphere with n double points and no simple loop.

Original entry on oeis.org

0, 0, 1, 1, 2, 9, 29, 133, 594, 2864

Offset: 1

N. J. A. Sloane, Mar 03 2016

Robert Coquereaux and Jean-Bernard Zuber, Maps, immersions and permutations, Journal of Knot Theory and Its Ramifications, Vol. 25, No. 8 (2016), 1650047; arXiv preprint, arXiv:1507.03163 [math.CO], 2015-2016. See Table 6.

Cf. A008986, A264761, A268569, A268570, A268571, A268572.

Name clarified by Andrey Zabolotskiy, Jun 09 2024

A268569 Number of immersions of unoriented circle into oriented sphere with n double points and no simple loop.

Original entry on oeis.org

0, 0, 1, 1, 2, 6, 19, 74, 320, 1469

Offset: 1

N. J. A. Sloane, Mar 03 2016

Robert Coquereaux and Jean-Bernard Zuber, Maps, immersions and permutations, Journal of Knot Theory and Its Ramifications, Vol. 25, No. 8 (2016), 1650047; arXiv preprint, arXiv:1507.03163 [math.CO], 2015-2016. See Table 6.

Cf. A008987, A264760, A268568, A268570, A268571, A268572.

Name clarified by Andrey Zabolotskiy, Jun 09 2024

A268570 Number of immersions of oriented circle into unoriented sphere with n double points and no simple loop.

Original entry on oeis.org

0, 0, 1, 1, 2, 5, 18, 70, 313, 1440

Offset: 1

N. J. A. Sloane, Mar 03 2016

Robert Coquereaux and Jean-Bernard Zuber, Maps, immersions and permutations, Journal of Knot Theory and Its Ramifications, Vol. 25, No. 8 (2016), 1650047; arXiv preprint, arXiv:1507.03163 [math.CO], 2015-2016. See Table 6.

Cf. A008988, A007756, A268568, A268569, A268571, A268572.

Name clarified by Andrey Zabolotskiy, Jun 09 2024

A289655 Subset of A008989 containing one or more simple loops.

Original entry on oeis.org

0, 1, 2, 5, 18, 74, 371, 2178

Offset: 0

N. J. A. Sloane, Jul 17 2017

It appears (although it is not certain) that A268571(n) = A008989(n) - a(n).

Guy Valette, A Classification of Spherical Curves Based on Gauss Diagrams, Arnold Math. J. (2016) 2:383-405, DOI 10.1007/s40598-016-0049-3.

Cf. A008989, A268571.

Showing 1-4 of 4 results.