A342646 Maximal number of 4213 patterns in a permutation of 1,2,...,n.

0, 0, 0, 0, 1, 3, 6, 13, 24, 40, 62, 96, 138, 192, 264, 354

Offset: 0

Author

Peter Kagey, Mar 20 2021

Keywords

• nonn
• more

Comments

Equivalently the maximal number of 1342, 2431, and 3124 patterns.

Examples

			For n = 7, a(7) = 13 because the permutation 7532146 has 13 instances of the pattern 4213, namely: 7536, 7526, 7516, 7546, 7324, 7326, 7314, 7316, 7214, 7216, 5324, 5314, and 5214.
Moreover, all other permutations in S_7 have 13 or fewer instances of this pattern.
		

Links

• M. H. Albert, M. D. Atkinson, C. C.Handley, D. A. Holton, and W. Stromquist, On packing densities of permutations, The Electronic Journal of Combinatorics, 9(1) (2002).
• David Bevan, The permutation class Av(4213,2143), arXiv:1510.06328 [math.CO], 2015.
• FindStat, St000750: The number of occurrences of the pattern 4213 in a permutation.
• Rob Pratt, Greatest number of occurrences of the pattern 4213 in a permutation, Mathematics Stack Exchange.
• Eric Weisstein's World of Mathematics, Permutation Pattern

Crossrefs

Analogous for other patterns: A000292 (123), A000332 (1234), A061061 (132), A100354 (1432).

Cf. A005802, A022558

Extensions

a(10)-a(12) from Rob Pratt

a(13)-a(15) from Bert Dobbelaere, Mar 26 2021