

A317486


Number of 6cycles in the nBruhat graph.


2



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

1,4


COMMENTS

In the nBruhat graph, 6cycles 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



FORMULA

a(n) = n!*((n2)/6 + (n3)*(n4)/2 + (n3)*(n4)*(n5)/3) for n > 2.  Andrew Howroyd, Jul 31 2018


EXAMPLE

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 6cycle that moves all 5 points:
(12345)>(21345)>(23145)>(23154)>(21354)>(12354)>(12345).
(End)


PROG

(PARI) a(n) = n!*if(n<3, 0, (n2)/6 + (n3)*(n4)/2 + (n3)*(n4)*(n5)/3); \\ Andrew Howroyd, Jul 31 2018


CROSSREFS

Cf. A300851 (6cycles in the transposition graph).
Cf. A317487 (4cycles in the Bruhat graph).


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



