login
A051496
Decimal expansion of the probability that a point of an infinite (rooted) tree is fixed by every automorphism of the tree.
0
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, 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, 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
OFFSET
0,1
COMMENTS
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...
LINKS
D. J. Broadhurst and D. Kreimer, Renormalization automated by Hopf algebra, arXiv:hep-th/9810087, 1998.
Frank Harary and Edgar M. Palmer, The probability that a point of a tree is fixed, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 3, 407-415.
FORMULA
Equals lim_{n->oo} A005200(n)/(n*A000081(n)).
Equals lim_{n->oo} A005201(n)/(n*A000055(n)).
EXAMPLE
0.6995388700609892332166312186...
CROSSREFS
KEYWORD
nonn,cons
STATUS
approved