A281259 Number of elements of S_n with strategic pile of size 6.

0, 0, 0, 0, 0, 0, 0, 1080, 12960, 143424, 1641600, 19915200, 257644800, 3556224000, 52289556480, 817133184000, 13536585216000, 237105792000000, 4380335511552000, 85148431867699200, 1737742314147840000, 37156364106301440000, 830772012055265280000

Offset: 1

Author

Marisa Gaetz, Jan 18 2017

Keywords

• nonn

Comments

Strategic pile is as defined in A267323.

The formula given below is a specific instance of the formula that will appear in "Quantifying CDS Sortability of Permutations Using Strategic Piles", see link.

Examples

			The permutation P = [3,5,1,8,6,2,7,4] has strategic pile of size 6. This can be found by the following cycle composition: (0,4,7,2,6,8,1,5,3)(0,1,2,3,4,5,6,7,8)=(0,5,8,4,3,7,1,6,2). Therefore, the strategic pile of P is {4,3,7,1,6,2}.
		

Links

• M. Gaetz, B. Molokach, M. Scheepers, and M. Shanks, Quantifying CDS Sortability of Permutations Using Strategic Piles
• Marisa Gaetz, Bethany Flanagan, Marion Scheepers, Meghan Shanks, Quantifying CDS Sortability of Permutations by Strategic Pile Size, arXiv:1811.11937 [math.CO], 2018.

Crossrefs

Cf. A267323 (size 3), A267324 (size 4), A267391 (size 5).

Formula

a(n) = (n-6)!*(120*binomial(n-7,5) + 576*binomial(n-7,4) + 1116*binomial(n-7,3) + 1080*binomial(n-7,2) + 540*binomial(n-7,1)) for n>7.