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

Author

N. J. A. Sloane, Nov 13 2009

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• Álvar Ibeas, Table of n, a(n) for n = 0..1829
• Michael W. Hero and Jeb F. Willenbring, Stable Hilbert series as related to the measurement of quantum entanglement, Discrete Mathematics, 309 (2009), 6508-6514. See Table 3.
• J. H. Kwak and J. Lee, Isomorphism classes of graph bundles. Can. J. Math., 42(4), 1990, pp. 747-761.
• 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.

Crossrefs

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

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

Cf. A057004.

Programs

Sage

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

Extensions

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