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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], (16-December-2014)

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

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Last modified November 23 00:33 EST 2017. Contains 295107 sequences.