3 citations · 3 across the 3 of their papers we have counts for
4 papers
Generating Permutations with Restricted Containers
Michael H. Albert, Cheyne Homberger, Jay Pantone +2
We investigate a generalization of stacks that we call -machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that…
The number of 1...d-avoiding permutations of length d+r for SYMBOLIC d but numeric r
Shalosh B. Ekhad, Nathaniel Shar, Doron Zeilberger
We use the Robinson-Schensted correspondence, followed by symbol-crunching, in order to derive explicit expressions for the quantities mentioned in the title. We follow it by numbe…
A Very Short (Bijective!) Proof of Touchard's Catalan Identity
Amitai Regev, Nathaniel Shar, Doron Zeilberger
A very short, bijective proof, of Touchard's Catalan identity is given, using Dyck paths.
The (Ordinary) Generating Functions Enumerating 123-Avoiding Words with r occurrences of each of 1,2, ..., n are Always Algebraic
Nathaniel Shar, Doron Zeilberger
Recently, Bill Chen, together with his disciples Alvin Dai and Robin Zhou, discovered, and very elegantly proved, an algebraic equation satisfied by the generating function enumera…