A306191 T(n,k) is a triangular array read by rows. Let S_n act on the set of size two subsets of {1,2,...,n}. T(n,k) is the number of permutations in S_n that fix exactly k size two subsets, n >= 1, 0 <= k <= binomial(n,2).

1, 0, 2, 2, 3, 0, 1, 14, 0, 9, 0, 0, 0, 1, 54, 40, 15, 0, 10, 0, 0, 0, 0, 0, 1, 304, 300, 0, 100, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 1, 2260, 1638, 630, 315, 0, 105, 70, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 18108, 12992, 5460, 1344, 1645, 0, 420, 0, 210, 0, 112, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Geoffrey Critzer, Jan 28 2019

Keywords

• nonn
• tabf

Comments

The action of S_n on the 2-subsets of {1,2,...,n} is defined: For all pi in S_n, pi({i,j}) = {pi(i),pi(j)}.

Examples

			1,
0,   2,
2,   3,   0,  1,
14,  0,   9,  0,   0,  0, 1,
54,  40,  15, 0,   10, 0, 0, 0,  0, 0, 1,
304, 300, 0,  100, 0,  0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 1,
		

Crossrefs

Cf. A137482 is column 1.

Programs

Mathematica

f[list_] := Flatten[Position[list /. x_ /; x > 0 -> 1, 1]];
Level[CoefficientList[Table[n! PairGroupIndex[SymmetricGroup[n], s] /. {Table[s[i] -> 1, {i, 2, Binomial[n, 2]}]}, {n, 1, 8}],
   s[1]], {2}] // Grid