OFFSET
1,8
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.
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.
EXAMPLE
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}.
CROSSREFS
KEYWORD
nonn
AUTHOR
Marisa Gaetz, Jan 18 2017
STATUS
approved