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A267385 Number of acyclic orientations of the Turán graph T(n,5). 2

%I #7 Feb 18 2017 08:35:22

%S 1,1,2,6,24,120,600,3720,27240,229080,2170680,20452440,217008600,

%T 2550317880,32808887160,457907248920,6355848354360,95721761831160,

%U 1551458493435480,26890032710452440,495810323060597880,9097662007250393880,177624183228083188440

%N Number of acyclic orientations of the Turán graph T(n,5).

%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="/A267385/b267385.txt">Table of n, a(n) for n = 0..450</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/Tur%C3%A1n_graph">Turán graph</a>

%F a(n) ~ n! / (4 * (1 - log(5/4))^2 * 5^n * (log(5/4))^(n+1)). - _Vaclav Kotesovec_, Feb 18 2017

%Y Column k=5 of A267383.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jan 13 2016

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)