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A051496 Decimal expansion of probability that a point of an infinite (rooted) tree is fixed by every automorphism of the tree. 0

%I

%S 6,9,9,5,3,8,8,7,0,0,6,0,9,8,9,2,3,3,2,1,6,6,3,1,2,1,8,6,2,0,1,4,2,7,

%T 6,7,1,6,3,6,8,1,4,5,5,4,6,3,5,4,2,1,6,1,9,8,9,7,5,9,2,2,0,3,2,0,0,4,

%U 6,4,1,9,2,5,6,2,9,5,6,1,2,1,4,8,7,8,4,8,0,6,0,2,8,2,6,5,4,8

%N Decimal expansion of probability that a point of an infinite (rooted) tree is fixed by every automorphism of the tree.

%C F. Harary and E. M. Palmer derive certain functional equations and, using the methods of G. Polya (Acta Math. 68 (1937), 145 254) and R. Otter (Ann. of Math. (2) 49 (1948), 583 - 599; Math. Rev. 10, 53), prove that the limiting probability of a fixed point in a large random tree, whether rooted or not, is 0.6995 ...

%D Harary, Frank; Palmer, Edgar M; The probability that a point of a tree is fixed; Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 3, 407-415.

%H D. J. Broadhurst and D. Kreimer, <a href="http://arXiv.org/abs/hep-th/9810087">Rooted-tree paper</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%e 0.6995388700609892332166312186...

%Y Equals \lim_{n\to\infty} A005200[n]/(n*A000081[n]) = \lim_{n\to\infty} A005201[n]/(n*A000055[n])

%K nonn,cons

%O 0,1

%A _David Broadhurst_

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)