The Expected Number of Blocks in an Ordered Set Partition of n objects is n/log(4)+O(1),
its Variance is (n/log(4))(1/log(4)-1/2)+O(1)
and It is Asymptotically Normal! (An Experimental-Mathematical Proof)
By Shalosh B. Ekhad
.pdf
.ps
.tex
Written: June 28, 2011.
This article was inspired by my master's
quickie
that was inspired, in turn by
Dan Haran's
Email message .
I was wondering what happens when you replace -1 by t, and asked about the statistical properties
of the distribution "number of blocks" in the poplulation of ordered set partitions.
The conclusions of this article were obtained by running the
input file
with the Maple program
OSP
(kindly written by Doron Zeilberger), that generated the
output file .
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
Doron Zeilberger's Home Page