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

1,3

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)}.

Links

Table of n, a(n) for n=1..92.

Example

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,

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

Crossrefs

Cf. A137482 is column 1.

Sequence in context: A182631 A231728 A303545 * A290125 A387381 A307356

Adjacent sequences: A306188 A306189 A306190 * A306192 A306193 A306194

Keyword

nonn,tabf

Author

Geoffrey Critzer, Jan 28 2019

Status

approved