A combinatorial interpretation for the identity Sum_k=0ⁿ binomnk Sum_j=0^k binomkj³= Sum_k=0ⁿ binomnk²binom2kk

2007/12/23 by David Callan, Callan, David
Mathematics · #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.0712.3946

4 pages

arxiv created 2007/12/23 · openalex publication_date 2007/12/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The title identity appeared as Problem 75-4, proposed by P. Barrucand, in Siam Review in 1975. The published solution equated constant terms in a suitable polynomial identity. Here we give a combinatorial interpretation in terms of card deals.

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