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 A370613 Total number of acyclic orientations in all complete multipartite graphs K_lambda, where lambda ranges over all partitions of n into distinct parts. 3
 1, 1, 1, 5, 9, 63, 509, 2959, 22453, 247949, 3080991, 28988331, 407320739, 5122243495, 82583577967, 1430027615585, 22556817627789, 395098668828675, 7979894546677853, 154786744386253387, 3355612019167352821, 78865333300205585345, 1769663675666499515751 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. All terms are odd. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171-178, doi:10.1016/0012-365X(73)90108-8 Wikipedia, Acyclic orientation Wikipedia, Multipartite graph MAPLE g:= proc(n) option remember; `if`(n=0, 1, add( expand(x*g(n-j))*binomial(n-1, j-1), j=1..n)) end: b:= proc(t, n, i) option remember; `if`(i*(i+1)/2 abs(b(0, n\$2)): seq(a(n), n=0..22); CROSSREFS Row sums of A370614. Cf. A000009, A267383, A372254, A372261, A372326, A372395. Sequence in context: A222536 A222698 A200440 * A347991 A179100 A358966 Adjacent sequences: A370610 A370611 A370612 * A370614 A370615 A370616 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 30 2024 STATUS approved

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Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)