A281723 - OEIS

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

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OFFSET

0,1

COMMENTS

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

LINKS

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

KEYWORD

nonn,hard,more

AUTHOR

STATUS

approved