A342853 Maximal number of 1324 patterns in a permutation of 1,2,...,n.

0, 0, 0, 0, 1, 3, 6, 13, 24, 42, 68, 106, 153, 217, 300

Offset: 0

Author

Peter Kagey, Mar 25 2021

Keywords

• nonn
• more

Comments

Equivalently the maximal number of 4231 patterns in a permutation of 1,2,...,n.

Examples

			For n = 5, the permutation 14325 has a(5) = 3 subsequences with the same relative order as 1324: 1435, 1425, and 1325.
All other permutations in S_5 have 3 or fewer such subsequences.
		

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).
• Miklós Bóna. A new record for 1324-avoiding permutations European Journal of Mathematics 1 (2015), 198-206.
• Anders Claesson, Vít Jelínek, and Einar Steingrímsson, Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns, Journal of Combinatorial Theory, Series A, 199.8 (2012), 1680-1691.
• FindStat, St000405: The number of occurrences of the pattern 1324 in a permutation.
• User Noodle9, answer to Patterns in Permutations, Code Golf Stack Exchange.
• Eric Weisstein's World of Mathematics, Permutation Pattern

Crossrefs

Analogous for other patterns: A000292 (123), A000332 (1234), A061061 (132), A100354 (1432), A342646 (4213), A342854 (2413).

Extensions

a(11) from Code Golf Stack Exchange link added by Peter Kagey, Mar 25 2021

a(12)-a(14) from Hugo Pfoertner, Mar 26 2021