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Number of 4-cycles in the n-Bruhat graph.
2

%I #12 Jul 06 2023 15:17:21

%S 0,0,0,6,90,1080,12600,151200,1905120,25401600,359251200,5388768000,

%T 85621536000,1438441804800,25499650176000,475993469952000,

%U 9336794987520000,192071211171840000,4135933413900288000,93058501812756480000,2184137777840578560000,53390034569436364800000

%N Number of 4-cycles in the n-Bruhat graph.

%H Andrew Howroyd, <a href="/A317487/b317487.txt">Table of n, a(n) for n = 1..200</a>

%H Jennifer Elder, Pamela E. Harris, Jan Kretschmann, and J. Carlos Martínez Mori, <a href="https://arxiv.org/abs/2306.14734">Boolean intervals in the weak order of S_n</a>, arXiv:2306.14734 [math.CO], 2023.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BruhatGraph.html">Bruhat Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>

%F a(n) = n!*(n-2)*(n-3)/8 for n > 1. - _Andrew Howroyd_, Jul 30 2018

%o (PARI) a(n) = if(n > 1, n!*(n-2)*(n-3)/8, 0); \\ _Andrew Howroyd_, Jul 30 2018

%Y Cf. A317486.

%K nonn

%O 1,4

%A _Eric W. Weisstein_, Jul 29 2018

%E Terms a(10) and beyond from _Andrew Howroyd_, Jul 30 2018