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A267388 Number of acyclic orientations of the Turán graph T(n,8). 2

%I #7 Feb 18 2017 08:37:38

%S 1,1,2,6,24,120,720,5040,40320,322560,2943360,30078720,339696000,

%T 4196666880,56255149440,812752093440,12585067447680,194465276369280,

%U 3220308737573760,56845456896816000,1064856592650695040,21087473349235547520,440007278378842984320

%N Number of acyclic orientations of the Turán graph T(n,8).

%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="/A267388/b267388.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! / (7 * (1 - log(8/7))^(7/2) * 8^n * (log(8/7))^(n+1)). - _Vaclav Kotesovec_, Feb 18 2017

%Y Column k=8 of A267383.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jan 13 2016

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)