OFFSET
0,3
COMMENTS
Conjectured to be the number of permutations of length n avoiding the partially ordered pattern (POP) {2>1>5>3, 5>4} of length 5. That is, conjectured to be the number of length n permutations having no subsequences of length 5 in which the elements 3 and 4 are the smallest, and the element in position 2 is larger than that in position 1, which in turn is larger than the element in position 5.- Sergey Kitaev, Dec 13 2020
Restatement of the comment by Kitaev: Conjectured to be the number of permutations of length n avoiding patterns 45123 and 45213. - Alexander Burstein, Feb 05 2024
LINKS
Jay Pantone, Table of n, a(n) for n = 0..790
Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Combinatorial Exploration: An algorithmic framework for enumeration, arXiv:2202.07715 [math.CO], 2022.
Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, PermPAL Database
Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); arXiv preprint, arXiv:2312.07716 [math.CO], 2023.
Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
B. Nakamura, Approaches for enumerating permutations with a prescribed number of occurrences of patterns, arXiv 1301.5080 [math.CO], 2013.
MAPLE
# Programs can be obtained from author's personal website.
CROSSREFS
KEYWORD
nonn
AUTHOR
Brian Nakamura, Apr 03 2013
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Dec 13 2020
STATUS
approved