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A262480
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Number of trivial c-Wilf equivalence classes in the symmetric group S_n.
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4
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1, 1, 1, 2, 8, 32, 192, 1272, 10176, 90816, 908160, 9980160, 119761920, 1556766720, 21794734080, 326918753280, 5230700052480, 88921859604480, 1600593472880640, 30411275148656640, 608225502973132800, 12772735543856332800, 281000181964839321600, 6463004184741681561600, 155112100433800357478400, 3877802510833236993638400
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OFFSET
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0,4
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COMMENTS
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A permutation pattern is c-Wilf equivalent to its complement and reverse and therefore we can get trivial equivalence classes based on complement and reverse. a(3) = 2 because there are two trivial c-Wilf equivalence classes {123, 321} and {132, 231, 213, 321}.
a(n) is an upper bound of c-Wilf equivalence classes in the symmetric group S_n.
The numbers of c-Wilf equivalence classes in S_n are still unknown for large n. Up to 6, they are 1, 1, 2, 7, 25, 92.
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LINKS
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Table of n, a(n) for n=0..25.
A. Duane, J. Remmel, Minimal overlapping patterns in colored permutations, Electron. J. Combin. 18 (2011) #P25.
B. Nakamura, Computational methods in permutation patterns, Ph. D. dissertation at Rutgers University, 2013.
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FORMULA
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a(0) = a(1) = 1, a(2*n) = ((2*n)!+(2*n)!!)/4, a(2*n+1) = ((2*n+1)!+(2*n)!!)/4, for n >= 1.
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CROSSREFS
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Cf. A000165, A000142.
Sequence in context: A294506 A206303 A048855 * A062797 A134751 A139014
Adjacent sequences: A262477 A262478 A262479 * A262481 A262482 A262483
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KEYWORD
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nonn
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AUTHOR
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Ran Pan, Sep 24 2015
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STATUS
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approved
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