A translation method for finding combinatorial bijections. 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.
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References in zbMATH (referenced in 3 articles )
Showing results 1 to 3 of 3.
- Steinhardt, Jacob: Permutations with ascending and descending blocks (2010)
- Gerdemann, Dale: Combinatorial proofs of Zeckendorf family identities (2009)
- Wood, Philip Matchett; Zeilberger, Doron: A translation method for finding combinatorial bijections (2009)