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

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

Author

David Broadhurst

Keywords

• nonn
• cons

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...

Examples

			0.6995388700609892332166312186...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.6.3, p. 304.

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.
• Index entries for sequences related to trees.
• Index entries for sequences related to rooted trees.

Crossrefs

Cf. A000055, A000081, A005200, A005201.

Formula

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

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