@article {IOPORT.05999913, author = {Wood, Philip Matchett and Zeilberger, Doron}, title = {A translation method for finding combinatorial bijections.}, year = {2009}, journal = {Annals of Combinatorics}, volume = {13}, number = {3}, issn = {0218-0006}, pages = {383-402}, publisher = {Birkh\"auser Verlag (Springer), Basel}, doi = {10.1007/s00026-009-0024-y}, abstract = {Summary: Consider a combinatorial identity that can be proved by induction. In this paper, we describe a general method for translating the inductive proof into a recursive bijection. Furthermore, we will demonstrate that the resulting recursive bijection can often be defined in a direct, non-recursive way. Thus, the translation method often results in a bijective proof of the identity that helps illuminate the underlying combinatorial structures. This paper has two main parts: First, we describe the translation method and the accompanying Maple code; and second, we give a few examples of how the method has been used to discover new bijections.}, identifier = {05999913}, }