login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A267323 The number of permutations in S_n with strategic pile of size 3. 3
0, 0, 0, 3, 12, 66, 432, 3240, 27360 (list; graph; refs; listen; history; text; internal format)
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], 2014-2017.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)