On Vince Vatter's Brilliant Extension of Doron Zeilberger's
Enumeration Schemes for Counting Herb Wilf's Classes
By Doron Zeilberger
.pdf
.ps
.tex
Exclusively published in the
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
First Written: Dec. 29, 2006.
Previous Version: March 26, 2007 (incorporating referee Lara Pudwell's
comments.)
This Version: March 28, 2007 (incorporating some of
referee Vince Vatter's comments.)
This is a modest improvement on
Vince Vatter's major improvement
of my
original enumeration schemes paper
My brilliant current student, Lara Pudwell, is currently extending this
to words (a.k.a. multiset permutations).
added March 26, 2007: Thoroughly refereed by Lara Pudwell.
Read
Lara Pudwell's report and
my response .
added March 28, 2007: Also thoroughly refereed by Vince Vatter.
Read
Vince Vatter's report and
my response .
Important: This article is accompanied by Maple
package
VATTER
that tries to find Vatter-Zeilberger-type enumeration schemes
for any set of patterns.
Sample Input and Output
-
In order to find enumeration schemes for single patterns of
length 3 the
input would yield the
output
-
In order to find enumeration schemes for a set of two patterns,
both of length 3, the
input would yield the
output
-
In order to find enumeration schemes for a set three patterns,
each of length 3 the
input would yield the
output
-
In order to find enumeration schemes for sets of four patterns of
each length 3 the
input would yield the
output
-
In order to find enumeration schemes for single patterns of
length 4 the
input would yield the
output
-
In order to find enumeration schemes for sets of two patterns
one of length 3 and the other of length 4, the
input would yield the
output
-
In order to find enumeration schemes for sets of two patterns
both of length 4, the
input would yield the
output
-
In order to find enumeration schemes for sets of two patterns ,
one of length 3 and the other of length 5, the
input would yield the
output
-
In order to find enumeration schemes for sets of three patterns ,
one of length 3 and the other two of length 4, the
input would yield the
output
-
In order to find enumeration schemes for sets of three patterns ,
one of length 4 and the other two of length 3, the
input would yield the
output
-
In order to find enumeration schemes for sets of three patterns ,
all of length 4 , the
input would yield the
output
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
Doron Zeilberger's Home Page