login
A342853
Maximal number of 1324 patterns in a permutation of 1,2,...,n.
2
0, 0, 0, 0, 1, 3, 6, 13, 24, 42, 68, 106, 153, 217, 300
OFFSET
0,6
COMMENTS
Equivalently the maximal number of 4231 patterns in a permutation of 1,2,...,n.
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.
User Noodle9, answer to Patterns in Permutations, Code Golf Stack Exchange.
Eric Weisstein's World of Mathematics, Permutation Pattern
EXAMPLE
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.
CROSSREFS
Analogous for other patterns: A000292 (123), A000332 (1234), A061061 (132), A100354 (1432), A342646 (4213), A342854 (2413).
Sequence in context: A374627 A058554 A342646 * A128517 A022568 A120006
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Mar 25 2021
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
STATUS
approved