... Beissinger, who was the first to explore [1] combinatorial proofs using colored permutations, for their assistance References [1] Janet Beissinger Colorful proofs of generating function identities ... follows for (π, f ) ∈ Sn,A : If R(π,f ) = ∅, let φ((π, f )) = (π, f ) Otherwise, let (i, j) ∈ R(π,f ) be minimal under the lexicographic ordering of R(π,f ) Let π = (i, j) ◦ π, the product of the ... 49 of Cambridge Studies in Advanced Mathematics Cambridge University Press, Cambridge, 1997 With a foreword by Gian-Carlo Rota, Corrected reprint of the 1986 original the electronic journal of...