Vol. 14, No. 4, 2021

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On proofs of certain combinatorial identities

Ryan Bianconi, Marcus Elia, Akalu Tefera and Aklilu Zeleke

Vol. 14 (2021), No. 4, 697–702
Abstract

We present combinatorial and computer-assisted proofs of identities that involve powers and products of binomial coefficients. A byproduct of our main result gives an alternate proof of Problem 11844 that appeared in the May 2015 issue of the American Mathematical Monthly.

Keywords
combinatorial identities, Gosper algorithm, Wilf–Zeilberger algorithm
Mathematical Subject Classification
Primary: 05A19
Milestones
Received: 4 January 2021
Accepted: 28 April 2021
Published: 23 October 2021

Communicated by Arthur T. Benjamin
Authors
Ryan Bianconi
Department of Mathematics
The University of Iowa
Iowa City, IA
United States
Marcus Elia
Department of Mathematics
The University of Vermont
Burlington, VT
United States
Akalu Tefera
Department of Mathematics
Grand Valley State University
Allendale, MI
United States
Aklilu Zeleke
Lyman Briggs College and Department of Statistics and Probability
Michigan State University
East Lansing, MI
United States