A372084 - OEIS

%I #19 Apr 27 2024 16:27:03

%S 1,1,14,122190,4154515368024,1835278052687560517522520,

%T 26375779571296696625528695444035039796080,

%U 25932533306693349690666903275634586837883421559437937952074800,3259525010466811026507391843042719132975543560928683870154345751824625274129141118944640

%N Number of acyclic orientations of the Turán graph T(n^2,n).

%C The Turán graph T(n^2,n) is the complete n-partite graph K_{n,...,n}.

%C An acyclic orientation is an assignment of a direction to each edge such that no cycle in the graph is consistently oriented. Stanley showed that the number of acyclic orientations of a graph G is equal to the absolute value of the chromatic polynomial X_G(q) evaluated at q=-1.

%H Alois P. Heinz, <a href="/A372084/b372084.txt">Table of n, a(n) for n = 0..21</a>

%H Richard P. Stanley, <a href="http://dx.doi.org/10.1016/0012-365X(73)90108-8">Acyclic Orientations of Graphs</a>, Discrete Mathematics, 5 (1973), pages 171-178, doi:10.1016/0012-365X(73)90108-8

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Acyclic_orientation">Acyclic orientation</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Multipartite_graph">Multipartite graph</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tur%C3%A1n_graph">Turán graph</a>

%F a(n) = A267383(n^2,n).

%Y Main diagonal of A372326.

%Y Cf. A267383.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Apr 17 2024