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
Keywords
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.
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.
Comments