A393920 - OEIS

%I #30 Jul 04 2026 17:59:31

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

%N 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.

%H Henning Krause and Balduin Stoye, <a href="https://arxiv.org/abs/2601.22649">Multisets of finite intervals and a universal category of poset representations</a>, arXiv:2601.22649 [math.RT], 2026.

%H Volodymyr Mazorchuk, <a href="https://arxiv.org/abs/2607.00651">On the number of extension closed additive subcategories for uniformly oriented A_n quivers</a>, arXiv:2607.00651 [math.RT], 2026. See pp. 1-3, 5.

%e 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).

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

%K nonn,more,changed

%O 1,1

%A _Henning Krause_, Mar 02 2026

%E a(7)-a(8) computed by _F. Chapoton_ added by _Henning Krause_, Apr 08 2026