Average Partial Order Width of the Divisor Poset

Summary: Determine the asymptotic behavior of G(n) := (g(1) + $\cdots$ + g(n))/n, where g(m) is the largest antichain in the divisor poset Dm. It is conjectured that G(n) = $\theta$(log n).

Classification: Primary, discrete mathematics; Secondary, other (posets, asymptotic enumeration)

Marko Riedel
EDV, Neue Arbeit gGmbH
Gottfried-Keller-Str. 18c
70435 Stuttgart, Germany
e-mail: mriedel@neuearbeit.de and markoriedelde@yahoo.de (preferred)

Tsz Ho Chan
Mathematical Sciences
The University of Memphis
373 Dunn Hall
Memphis, TN 38152-3240
e-mail: tszchan@memphis.edu

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