A160449 Array read by antidiagonals: T(n,k) is the number of isomorphism classes of n-fold coverings of a connected graph with Betti number k (1 <= n, 0 <= k).

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 5, 11, 8, 1, 1, 7, 43, 49, 16, 1, 1, 11, 161, 681, 251, 32, 1, 1, 15, 901, 14721, 14491, 1393, 64, 1, 1, 22, 5579, 524137, 1730861, 336465, 8051, 128, 1, 1, 30, 43206, 25471105, 373486525, 207388305, 7997683, 47449, 256, 1

Offset

0,5

Comments

T(n,k) is the number of orbits of the conjugacy action of Sym(n) on Sym(n)^k [Kwak and Lee, 2001]. - Álvar Ibeas, Mar 25 2015

References

J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161. See Table 2.

Links

Álvar Ibeas, Table of n, a(n) for n = 0..1829

J. H. Kwak and J. Lee, Isomorphism classes of graph bundles. Can. J. Math., 42(4), 1990, pp. 747-761.

Example

The array begins:
    k=0   k=1   k=2   k=3     k=4       k=5
n=1   1     1     1     1       1         1
n=2   1     2     4     8      16        32
n=3   1     3    11    49     251      1393
n=4   1     5    43   681   14491    336465
n=5   1     7   161 14721 1730861 207388305

Prog

(Sage)
def A160449(n, k):
    return sum(p.aut()**(k - 1) for p in Partitions(n))
# Álvar Ibeas, Mar 25 2015

Crossrefs

Rows: A000012, A000079, A074528, A160450, A160454, A176709.

Columns: A000041, A110143, A152612, A160446, A160447, A160448.

Cf. A057004.

Sequence in context: A321877 A320251 A210341 * A326322 A089940 A331598

Adjacent sequences: A160446 A160447 A160448 * A160450 A160451 A160452

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 13 2009

Extensions

Name clarified and more terms added by Álvar Ibeas, Mar 25 2015

Status

approved