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A267323 The number of permutations in S_n with strategic pile of size 3. 4
0, 0, 0, 3, 12, 66, 432, 3240, 27360 (list; graph; refs; listen; history; text; internal format)



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).


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.


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.


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




Marion Scheepers, Jan 13 2016



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