A Combinatorial Proof of an Alternating Convolution Identity for Multichoose Numbers

作者:Lutgen Jeffrey*
来源:American Mathematical Monthly, 2016, 123(2): 192-196.
DOI:10.4169/amer.math.monthly.123.2.192

摘要

We give a combinatorial proof for an identity involving an alternating sum of products of multichoose numbers. In our proof, we construct a sign-reversing involution on certain ordered pairs of words, then count the leftovers. We also outline two alternative proofs, one using hypergeometric functions and the other using mechanical summation.

  • 出版日期2016-2

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