A291371 Number of maximal chord diagrams of genus g counted up to rotations and reflections.

1, 4, 82, 7258, 1491629, 506855279, 254118439668, 176377605783906, 162019808170348933, 190375587419231088550, 278587959330563466969926, 496903413656110608290219603

Offset: 1

Author

Evgeniy Krasko, Sep 03 2017

Keywords

• nonn

Comments

Also the number of non-isomorphic one-face one-vertex maps on a genus g surface where both orientation-preserving and orientation-reversing isomorphisms are taken into account.

Links

• Evgeniy Krasko, Counting Unlabelled Chord Diagrams of Maximal Genus, arXiv:1709.00796 [math.CO], 2017.
• Evgeny Krasko, A. Omelchenko, Enumeration of Chord Diagrams without Loops and Parallel Chords, arXiv preprint arXiv:1601.05073 [math.CO], 2016; Electronic Journal of Combinatorics 24(3) (2017), #P3.43

Crossrefs

Maximal diagrams up to rotations: A291172.

Programs

Python

# Python version 2.7
rot_sym = [
  0, 1, 4, 131, 14118, 2976853, 1013582110, 508233789579, 352755124921122,
  324039613564554401, 380751174738424280720, 557175918657122229139987,
  993806827312044893602464496, # A291172
]
def u(n):
  if n < 0:
    return 0
  if n <= 1:
    return 1
  sum = 0
  sum -= (4 * n - 1) * u(n - 1)
  sum += n * (2 * n - 3) * (10 * n - 9) * u(n - 2)
  sum += 5 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * u(n - 3)
  sum -= 2 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * (2 * n - 6) * (2 * n - 7) * u(n - 4)
  return sum / (n + 1)
for i in range(1, 13):
  print (2 * rot_sym[i] + u(i) + u(i - 1) * (2 * i - 1)) / 4