An Involution Proof of the Alladi-Gordon Key Identity for Schur's Partition Theorem


The Alladi-Gordon identity ∑j k=0(q i−k+1; q)k [ j k ] q(i−k)(j−k) = 1 plays an important role for the Alladi-Gordon generalization of Schur’s partition theorem. By using Joichi-Stanton’s insertion algorithm, we present an overpartition interpretation for the Alladi-Gordon key identity. Based on this interpretation, we further obtain a combinatorial proof… (More)