A317486 Number of 6-cycles in the n-Bruhat graph.

0, 0, 1, 8, 180, 4080, 74760, 1249920, 20381760, 335059200, 5648227200, 98514662400, 1786117132800, 33737998694400, 664516524672000, 13648633270272000, 292197222180864000, 6515482307862528000, 151184585624776704000, 3646920110256783360000

Offset

1,4

Comments

In the n-Bruhat graph, 6-cycles can be of three types: 1) those that move only three adjacent points of the permutation, 2) those that move five points with two being adjacent and the other three being adjacent, 3) those that move a total of six points consisting of three pairs of adjacent points. - Andrew Howroyd, Jul 31 2018

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Bruhat Graph

Eric Weisstein's World of Mathematics, Graph Cycle

Formula

a(n) = n!*((n-2)/6 + (n-3)*(n-4)/2 + (n-3)*(n-4)*(n-5)/3) for n > 2. - Andrew Howroyd, Jul 31 2018

Example

From Andrew Howroyd, Jul 31 2018: (Start)
Case n=3: Vertices are permutations on S_3. There is only one cycle:
  (123)->(213)->(231)->(321)->(312)->(132)->(123).
Case n=5: An example of a 6-cycle that moves all 5 points:
  (12345)->(21345)->(23145)->(23154)->(21354)->(12354)->(12345).
(End)

Prog

(PARI) a(n) = n!*if(n<3, 0, (n-2)/6 + (n-3)*(n-4)/2 + (n-3)*(n-4)*(n-5)/3); \\ Andrew Howroyd, Jul 31 2018

Crossrefs

Cf. A300851 (6-cycles in the transposition graph).

Cf. A317487 (4-cycles in the Bruhat graph).

Sequence in context: A300255 A108552 A221589 * A360340 A060593 A130775

Adjacent sequences: A317483 A317484 A317485 * A317487 A317488 A317489

Keyword

nonn

Author

Eric W. Weisstein, Jul 29 2018

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jul 31 2018

Status

approved