[seqfan] Not in OEIS: decimal digits of 1/(2*e*pi), arises in "Asymptotic enumeration of sparse 2-connected graphs "

Jonathan Post jvospost3 at gmail.com
Thu Oct 14 05:50:38 CEST 2010


decimal digits of 1/(2*e*pi) ~ 0.05854983152

Given in Theorem 2(c), p.4, of Graeme Kemkes, Cristiane M. Sato,
Nicholas Wormald, "Asymptotic enumeration of sparse 2-connected graphs
Oct 12, 2010.

Abstract: We determine an asymptotic formula for the number of
labelled 2-connected (simple) graphs on n vertices and  edges,
provided that m-n approaches infinity and m=O(n log n) as n approaches
infinity. This is the entire range of m not covered by previous
results. The proof involves determining properties of the core and
kernel of random graphs with minimum degree at least 2. The case of
2-edge-connectedness is treated similarly. We also obtain formulae for
the number of 2-connected graphs with given degree sequence for most
(`typical') sequences. Our main result solves a problem of Wright from
1983 and determines his (mysterious) constant a to be 1/(2 e pi).

easy, constant, more

Cf. A001113 (decimal expansion of e, Euler's constant), A000796
(decimal expansion of Pi), A019609 Decimal expansion of Pi*E.

what is proper offset?

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