By Doron Zeilberger
In order to view the ordinary generating functions (that happen to be rational functions) for
the number of ways of reassembling one n-shelled, two identical n-shelled,
and three identical n-shelled Russian Dolls into k dolls, for small k,
Doron Zeilberger's List of other Papers
.pdf
.ps
.tex
Written: Sept. 16, 2009.
Dedicated to Thotsaporn and Thotsaphon Thanatipanonda
Exclusively published in the
Personal Journal of Ekhad and Zeilberger
and at arxiv.org.
When my brilliant student Thotsaporn "Aek" Thanatipanonda asked me about how many ways can
one cover n pairs of identical twins, it rang a Bell back to 1981 (see the article).
As usual, the method of teaching the computer how to do its own combinatorics,
and to use "analysis" (that is really part of discrete math) to enumerate challenging
combinatorial objects is even more interesting than the theorems and even
the algorithm. Of course, formulas are dead, long live algorithms! But even algorithms are dead,
long live meta-algorithms!!
Maple Packages
Important: This article is accompanied by Maple
package
Sample Input and Output for BABUSHKAS
the
input
gives the output.
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the input
gives the output.
the input
gives the output.
the input
gives the output.
the input
gives the output.
the input
gives the output.
the input
gives the output.
Personal Journal