Geodesic
An involution proof of the Alladi-Gordon key identity for Schur's partition theorem
James J.Y. Zhao1
1Dongling School of Economics and Management University of Science and Technology Beijing Beijing 100083 P.R. China
The electronic journal of combinatorics, Tome 20 (2013) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

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.
DOI : 10.37236/2826
Classification : 05A17, 05A19
Mots-clés : the Alladi-Gordon key identity, Joichi-Stanton's insertion algorithm, Schur's partition theorem, overpartitions

James J.Y. Zhao  1

1 Dongling School of Economics and Management University of Science and Technology Beijing Beijing 100083 P.R. China 
@article{10_37236_2826,
     author = {James J.Y. Zhao},
     title = {An involution proof of the {Alladi-Gordon} key identity for {Schur's} partition theorem},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {1},
     doi = {10.37236/2826},
     zbl = {1267.05034},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2826/}
}
TY  - JOUR
AU  - James J.Y. Zhao
TI  - An involution proof of the Alladi-Gordon key identity for Schur's partition theorem
JO  - The electronic journal of combinatorics
PY  - 2013
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/2826/
DO  - 10.37236/2826
ID  - 10_37236_2826
ER  - 
%0 Journal Article
%A James J.Y. Zhao
%T An involution proof of the Alladi-Gordon key identity for Schur's partition theorem
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2826/
%R 10.37236/2826
%F 10_37236_2826
James J.Y. Zhao. An involution proof of the Alladi-Gordon key identity for Schur's partition theorem. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2826

Cité par Sources :