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On proofs of certain combinatorial identities.(English)Zbl 1243.05038

The authors prove three combinatorial identities using both combinatorial proofs (involutions in some subsets of words) and WZ(Wilf-Zeilberger) method proofs. One of them is \[\sum _{k=0}^{n+1}(-1)^{n+k+1}{{n+k+1}\choose{2k}}2^{2k}=2n+3.\] Five other identities are deduced as corollaries.

MSC:

05A19 Combinatorial identities, bijective combinatorics

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