

A267323


The number of permutations in S_n with strategic pile of size 3.


4




OFFSET

1,4


COMMENTS

The strategic pile of permutation P=[a_1,...,a_n] is obtained from the disjoint cycle decomposition of the composition of the cycles (a_n, ..., a_1,0)(0,1, 2, ..., n). If 0 and n are not in the same cycle, the strategic pile of P is empty. Else, the terms appearing from n to 0, not including n or 0, in the cycle (n, ..., 0, ...) is the strategic pile of P.
The strategic pile of P=[3,2,4,1] is {1, 2, 3} which has size 3 because: (1,4,2,3,0)(0,1,2,3,4) = ( 4, 1, 3, 2, 0).


LINKS

Table of n, a(n) for n=1..9.
K. L. M. Adamyk, E. Holmes, G. R. Mayfield, D. J. Moritz, M. Scheepers, B. E. Tenner, H. C. Wauck, Sorting Permutations: Games, Genomes, and Cycles, arXiv:1410.2353 [math.CO], 20142017.
Marisa Gaetz, Bethany Flanagan, Marion Scheepers, Meghan Shanks, Quantifying CDS Sortability of Permutations by Strategic Pile Size, arXiv:1811.11937 [math.CO], 2018.


EXAMPLE

a(4) = 3 because [3,2,4,1], [2,4,1,3] and [4,1,3,2] are the only elements of S_4 that each has a strategic pile of size 3.


CROSSREFS

A267324 gives the corresponding sequence for strategic piles of size 4.
A267391 gives the corresponding sequence for strategic piles of size 5.
Sequence in context: A290147 A007871 A214565 * A058790 A199746 A293302
Adjacent sequences: A267320 A267321 A267322 * A267324 A267325 A267326


KEYWORD

nonn,more


AUTHOR

Marion Scheepers, Jan 13 2016


STATUS

approved



