A short proof of a famous combinatorial identity

2013/07/25 by Rui Duarte, Duarte, Rui, António Guedes de Oliveira +1
Computer Science · Mathematics · #05A19 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A19 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1307.6693

arxiv created 2013/07/25 · openalex publication_date 2013/07/25 · arxiv updated 2013/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explain how the identity ∑_i+j=n\binom2ii\binom2jj = 4ⁿ is an easy consequence of the inclusion-exclusion principle.

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