A214816
Number of unsensed combinatorial maps with n edges on an orientable surface of any genus.
Original entry on oeis.org
1, 2, 5, 20, 96, 644, 5839, 67834, 970568, 16256556, 308620966, 6506035400, 150358570914, 3775903806928, 102348067516576, 2977979542305736, 92579723269733557, 3062602106878957610, 107418879166917701583, 3981908920500346885116, 155550644128029095714786
Offset: 0
- Andrew Howroyd, Table of n, a(n) for n = 0..30
- Antonio Breda d'Azevedo, Alexander Mednykh, and Roman Nedela, Enumeration of maps regardless of genus: Geometric approach, Discrete Mathematics, Volume 310, 2010, Pages 1184-1203.
- Timothy R. Walsh, Space-efficient generation of nonisomorphic maps and hypermaps.
- T. R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3.
Cf.
A006385,
A006387,
A170946 (sensed),
A170947 (achiral),
A170948 (chiral pairs),
A214814,
A214815,
A297880,
A297881,
A348798,
A348800,
A348801.
A170946
Number of sensed unrooted combinatorial maps with n edges.
Original entry on oeis.org
1, 2, 5, 20, 107, 870, 9436, 122840, 1863359, 32019826, 613981447, 12989756316, 300559406027, 7550660328494, 204687564072918, 5955893472990664, 185158932576089787, 6125200100394894738, 214837724735760642773, 7963817561236130021156, 311101285883236139915989
Offset: 0
- Andrew Howroyd, Table of n, a(n) for n = 0..400 (terms 1..30 from Antonio Breda d'Azevedo, Alexander Mednykh and Roman Nedela)
- Antonio Breda d'Azevedo, Alexander Mednykh and Roman Nedela, Enumeration of maps regardless of genus: Geometric approach, Discrete Mathematics, Volume 310, 2010, Pages 1184-1203.
- N. M. Adrianov, N. Ya. Amburg, V. A. Dremov, Yu. A. Levitskaya, E. M. Kreines, Yu. Yu. Kochetkov, V. F. Nasretdinova and G. B. Shabat, Catalog of dessins d'enfants with <= 4 edges, arXiv:0710.2658 [math.AG], 2007.
- R. J. Mathar, Feynman diagrams of the QED vacuum polarization, vixra:1901.0148 (2019), Section V. Computed up to a(5), plotted up to a(4).
- R. de Mello Koch and S. Ramgoolam, Strings from Feynman graph counting: without large N, Phys Rev D, 85 (2012) 026007; arXiv:1110.4858 [hep-th], 2011-2012. The terms in Eq. (D.10) from a(7) on are erroneous.
A380234
Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).
Original entry on oeis.org
1, 2, 4, 1, 14, 6, 47, 34, 4, 184, 188, 46, 761, 1040, 408, 33, 3314, 5756, 3220, 538, 14997, 32069, 23824, 6489, 398, 69886, 179408, 169336, 66150, 8506, 333884, 1009234, 1170654, 611278, 129030, 6405, 1626998, 5700548, 7930892, 5279172, 1608172, 168702, 8067786, 32341002, 52930196, 43429578, 17758601, 3080190, 128448
Offset: 0
Triangle starts:
n\k [0] [1] [2] [3] [4]
[0] 1;
[1] 2;
[2] 4, 1;
[3] 14, 6;
[4] 47, 34, 4;
[5] 184, 188, 46;
[6] 761, 1040, 408, 33;
[7] 3314, 5756, 3220, 538;
[8] 14997, 32069, 23824, 6489, 398;
[9] 69886, 179408, 169336, 66150, 8506;
...
A170948
Number of chiral pairs of combinatorial maps with n edges.
Original entry on oeis.org
0, 0, 0, 0, 11, 226, 3597, 55006, 892791, 15763270, 305360481, 6483720916, 150200835113, 3774756521566, 102339496556342, 2977913930684928, 92579209306356230, 3062597993515937128, 107418845568842941190, 3981908640735783136040, 155550641755207044201203
Offset: 0
Name clarified, a(0)=0 prepended and a(19) onwards added by
Andrew Howroyd, Jan 27 2025
A380617
Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.
Original entry on oeis.org
1, 1, 1, 2, 2, 1, 5, 8, 5, 2, 16, 28, 26, 12, 3, 53, 121, 128, 82, 28, 6, 206, 528, 686, 505, 239, 68, 10, 817, 2516, 3638, 3192, 1802, 686, 157, 20, 3620, 12302, 20250, 19976, 13268, 6078, 1876, 372, 35, 16361, 63643, 114669, 126876, 95422, 50954, 19346, 5100, 845, 70
Offset: 0
Triangle begins:
n\k | 1 2 3 4 5 6 7 8 9
----+-------------------------------------------------------
0 | 1;
1 | 1, 1;
2 | 2, 2, 1;
3 | 5, 8, 5, 2;
4 | 16, 28, 26, 12, 3;
5 | 53, 121, 128, 82, 28, 6;
6 | 206, 528, 686, 505, 239, 68, 10;
7 | 817, 2516, 3638, 3192, 1802, 686, 157, 20;
8 | 3620, 12302, 20250, 19976, 13268, 6078, 1876, 372, 35;
...
Showing 1-5 of 5 results.
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