# Bijective proofs of Gould-Mohanty's and Raney-Mohanty's identities - Mathematics > Combinatorics

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Abstract: Using the model of words, we give bijective proofs of Gould-Mohanty-s andRaney-Mohanty-s identities, which are respectively multivariablegeneralizations of Gould-s identity $$\sum {k=0}^{n}{x-kz\choose k}{y+kz\choosen-k}= \sum {k=0}^{n}{x+\epsilon-kz\choose k}{y-\epsilon+kz\choose n-k} $$ andRothe-s identity $$ \sum {k=0}^{n}\frac{x}{x-kz}{x-kz\choose k}{y+kz\choosen-k}= {x+y\choose n}. $$

Author: ** Victor J. W. Guo**

Source: https://arxiv.org/