A Bijective Proof of and Identity Extending a Classic Result of Hajos

Abstract

We provide bijective proofs of two classic identities that are very simple to prove using generating functions, but surprisingly difficult to prove combinatorially. The problem of finding a bijective proof for the first identity was first raised in the 1930s. The second, more involved identity takes the first one a step further.

arXiv comment11 pages, 7 figures