A051496 - OEIS

%I #19 Apr 30 2023 02:10:31

%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 the 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. (1937) Vol. 68, 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...

%H D. J. Broadhurst and D. Kreimer, <a href="http://arXiv.org/abs/hep-th/9810087">Renormalization automated by Hopf algebra</a>, arXiv:hep-th/9810087, 1998.

%H Frank Harary and Edgar M. Palmer, <a href="https://doi.org/10.1017/S0305004100055857">The probability that a point of a tree is fixed</a>, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 3, 407-415.

%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>

%F Equals lim_{n->oo} A005200(n)/(n*A000081(n)).

%F Equals lim_{n->oo} A005201(n)/(n*A000055(n)).

%e 0.6995388700609892332166312186...

%Y Cf. A000055, A000081, A005200, A005201.

%K nonn,cons

%O 0,1

%A _David Broadhurst_