Keywords:
the Alladi-Gordon key identity, Joichi-Stanton's insertion algorithm, Schur's celebrated partition theorem, overpartitions
Abstract
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 overpartition interpretation for the Alladi-Gordon key identity. Based on this interpretation, we further obtain a combinatorial proof of the Alladi-Gordon key identity by establishing an involution on the underlying set of overpartitions.
Author Biography
James J.Y. Zhao, Dongling School of Economics and Management
University of Science and Technology Beijing
Beijing 100083
P.R. China
Lecturer
Dongling School of Economics and Management
University of Science and Technology Beijing
Beijing 100083
P.R. China