cp's OEIS Frontend

A007984 Number of essential graphs with n nodes (in 1-1 correspondence with Markov equivalence classes of acyclic digraphs).

%I A007984 #29 Jan 30 2025 11:21:48
%S A007984 1,2,11,185,8782,1067825,312510571,212133402500,326266056291213,
%T A007984 1118902054495975181,8455790399687227104576,
%U A007984 139537050182278289405732939,4991058955493997577840793161279
%N A007984 Number of essential graphs with n nodes (in 1-1 correspondence with Markov equivalence classes of acyclic digraphs).
%D A007984 S. B. Gillispie and M. D. Perlman, Enumerating Markov equivalence classes of acyclic digraph models, Proc. of Conf. on Uncertainty in Artificial Intelligence (2001), 171-177.
%D A007984 S. B. Gillispie and M. D. Perlman, The size distribution for Markov equivalence classes of acyclic digraph models, Artificial Intelligence, 141 (2002), 137-155.
%D A007984 Bertran Steinsky, Enumeration of Labelled Essential Graphs, Ars Comb., 111, (2013), 485-494
%H A007984 S. B. Gillispie and M. D. Perlman, <a href="http://stat.washington.edu/www/research/reports/2001/tr392.pdf">Enumerating Markov equivalence classes of acyclic digraph models</a>, Univ. of Washington, Dept. of Statistics, Technical Reports.
%H A007984 S. B. Gillispie and M. D. Perlman, <a href="http://stat.washington.edu/www/research/reports/2001/tr400.pdf">The size distribution for Markov equivalence classes of acyclic digraph models</a>, Univ. of Washington, Dept. of Statistics, Technical Reports.
%H A007984 Zehao Jin, Mario Pasquato, Benjamin L. Davis, Tristan Deleu, Yu Luo, Changhyun Cho, Pablo Lemos, Laurence Perreault-Levasseur, Yoshua Bengio, Xi Kang, Andrea Valerio Maccio, and Yashar Hezaveh, <a href="https://arxiv.org/abs/2410.00965">A Data-driven Discovery of the Causal Connection between Galaxy and Black Hole Evolution</a>, arXiv:2410.00965 [astro-ph.GA], 2024. See p. 33.
%H A007984 Zehao Jin, Mario Pasquato, Benjamin L. Davis, Tristan Deleu, Yu Luo, Changhyun Cho, Pablo Lemos, Laurence Perreault-Levasseur, Yoshua Bengio, and Xi Kang, <a href="https://doi.org/10.3847/1538-4357/ad9ded">Causal Discovery in Astrophysics: Unraveling Supermassive Black Hole and Galaxy Coevolution</a>, Astrophys. J. (2025) Vol. 979, 212. See Fig. 7.
%Y A007984 Cf. A368569 (refined by # arcs).
%K A007984 nonn
%O A007984 1,2
%A A007984 David Madigan (madigan(AT)stat.washington.edu)
%E A007984 More terms from Steven B. Gillispie (gillisp(AT)u.washington.edu), Oct 21 2003
%E A007984 a(10) corrected by Steven B. Gillispie (gillisp(AT)u.washington.edu), Aug 14 2007, who says: I have learned from _Bertran Steinsky_ (who determined the correct number) that there was an error in my computer software that computed a(10). The correct value is 1118902054495975181.
%E A007984 a(11)-a(13) from _Bertran Steinsky_, Jun 24 2013