DiscreteMath`CombinatorialSimplification`
=========================================

This package introduces elementary rules for simplifying ratios of
factorials, products and binomial coefficients when the arguments
are symbolic or non-numerical.  The rules are intended to cover
some of the more common situations that arise in combinatorial
analysis.  The built-in functions Factorial, Binomial, and Product
are affected by loading this package.

This loads the package.

     In[1]:= <<DiscreteMath`CombinatorialSimplification`
     


This ratio of factorials can be simplified without specifying the
value of n.

     In[2]:= (n+5)! / n!
     Out[2]= (1 + n) (2 + n) (3 + n) (4 + n) (5 + n)
     


Here is another combination of factorials that can be simplified.

     In[3]:= n! (n + 1) (n + 2)
     Out[3]= (2 + n)!
     


Here is a common ratio of binomial coefficients.

     In[4]:= Binomial[n, k]/Binomial[n, k - 1]
             1 - k + n
     Out[4]= ---------
                 k
     


This result uses an elementary property of products.

     In[5]:= Product[f[k], {k, 0, n + 1, 1}]/
                  Product[f[k], {k, 0, n, 1}]
     Out[5]= f[1 + n]