Gould-Mohanty恒等式和Raney-Mohanty恒等式的双射证明
Bijective proofs of Gould-Mohanty's and Raney-Mohanty's identities
摘要：
利用词的模型给出了Gould-Mohanty恒等式和Raney-Mohanty恒等式的双射证明，它们分别是Gould恒等式$$\sum_{k=0}^{n}{x-kz\choose k}{y+kz\choose n-k}= \sum_{k=0}^{n}{x+ε-kz\choose k}{y-ε+kz\choose n-k} $$和Rothe恒等式$$ \sum_{k=0}^{n}\frac{x}{x-kz}{x-kz\choose k}{y+kz\choose n-k}= {x+y\choose n}. $$的多元推广
英文摘要：
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 $$\sum_{k=0}^{n}{x-kz\choose k}{y+kz\choose n-k}= \sum_{k=0}^{n}{x+ε-kz\choose k}{y-ε+kz\choose n-k} $$ and Rothe's identity $$ \sum_{k=0}^{n}\frac{x}{x-kz}{x-kz\choose k}{y+kz\choose n-k}= {x+y\choose n}. $$
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