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    Bijective proofs of Gould-Mohanty's and Raney-Mohanty's identities

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    Using the model of words, we give bijective proofs of Gould-Mohanty's and Raney-Mohanty's identities, which are respectively multivariable generalizations of Gould's identity βˆ‘k=0n(xβˆ’kzk)(y+kznβˆ’k)=βˆ‘k=0n(x+Ο΅βˆ’kzk)(yβˆ’Ο΅+kznβˆ’k)\sum_{k=0}^{n}{x-kz\choose k}{y+kz\choose n-k}= \sum_{k=0}^{n}{x+\epsilon-kz\choose k}{y-\epsilon+kz\choose n-k} and Rothe's identity βˆ‘k=0nxxβˆ’kz(xβˆ’kzk)(y+kznβˆ’k)=(x+yn). \sum_{k=0}^{n}\frac{x}{x-kz}{x-kz\choose k}{y+kz\choose n-k}= {x+y\choose n}. Comment: 7 pages, to appear in Ars Combi
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