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

[摘要] The Alladi-Gordon identity $\sum_{k=0}^{j}(q^{i-k+1};q)_k\, {j \brack k} q^{(i-k)(j-k)}=1$ plays an important role for the Alladi-Gordon generalization of Schur's partition theorem. By using Joichi-Stanton's insertion algorithm, we present an overpartitio

[学科分类] 离散数学和组合数学

[关键词] the Alladi-Gordon key identity;Joichi-Stanton's insertion algorithm;Schur's celebrated partition theorem;overpartitions