A393920 Number of full subcategories of the category of finite dimensional linear representations of a totally ordered set with n elements (over any field) that are closed under extensions and direct summands.

2, 7, 34, 199, 1308, 9300, 69978, 549559

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Henning Krause and Balduin Stoye, Multisets of finite intervals and a universal category of poset representations, arXiv:2601.22649 [math.RT], 2026.

Volodymyr Mazorchuk, On the number of extension closed additive subcategories for uniformly oriented A_n quivers, arXiv:2607.00651 [math.RT], 2026. See pp. 1-3, 5.

Example

For a(n) an obvious upper bound is 2^m, where m=(n^2+n)/2 is the number of indecomposable representations. Thus a(2)=7 means there is one subset of the set of 3 indecomposable representations that is not extension closed. It is actually the set consisting of the two simple representations (there are always n simple representations).

Crossrefs

Cf. A000108 (quotient and extension closed subcategories), A000142 (quotient closed subcategories).

Sequence in context: A199475 A241599 A356118 * A307696 A237645 A117399

Adjacent sequences: A393917 A393918 A393919 * A393921 A393922 A393923

Keyword

nonn,more,changed

Author

Henning Krause, Mar 02 2026

Extensions

a(7)-a(8) computed by F. Chapoton added by Henning Krause, Apr 08 2026

Status

approved