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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
P = [7, 1, 5, 6, 2, 4, 3] has strategic pile size 5. The composition (0,3,4,2,6,5,1,7)(0,1,2,3,4,5,6,7) has cycle (7,3,2,4,1,6,0), and so the strategic pile of P is {1,2,3,4,6}.
CROSSREFS
A267323 gives the corresponding sequence for strategic piles of size 3.
A267324 gives the corresponding sequence for strategic piles of size 4.