A281723 Smallest positive integer that cannot be obtained as the number of linear extensions of a poset of size n.

2, 2, 3, 4, 7, 13, 17, 59, 253, 979

Offset

0,1

Comments

a(n) is the smallest positive integer such that A160371(a(n)) > n.

Links

Table of n, a(n) for n=0..9.

Swee Hong Chan and Igor Pak, Computational complexity of counting coincidences, arXiv:2308.10214 [math.CO], 2023. See p. 12.

Swee Hong Chan and Igor Pak, Linear extensions and continued fractions, arXiv:2401.09723 [math.CO], 2024.

Example

a(8) = 253, so the number 253 cannot be obtained as the number of linear extensions of a poset of size 8, but every integer from 1 to 252 can.

Crossrefs

Cf. A160371.

Sequence in context: A051920 A286350 A023105 * A011784 A302487 A032252

Adjacent sequences: A281720 A281721 A281722 * A281724 A281725 A281726

Keyword

nonn,hard,more

Author

François Labelle, Jan 28 2017

Status

approved