On Vince Vatter’s Brilliant Extension of Doron Zeilberger’s Enumeration Schemes for Herb Wilf ’s Classes

Zeilberger’s original approach My original approach was to teach the computer some elementary ‘logical reasoning’, and find enumeration schemes that way. This was done in a Maple package (still available from my website) called WILF. To check the ‘logical’ program, I also wrote an empirical program, called HERB. The Maple package HERB found enumeration schemes by testing them for permutations of size n ≤ N0, where N0 was some positive integer chosen by the user. But to rigorously prove the validity of the candidate enumeration schemes we still need the ‘logical’ program WILF, since the empirical program, HERB, is just that, empirical! OR IS IT?.