TY - JOUR
T1 - The Rogers-Ramanujan-Gordon identities, the generalized Göllnitz-Gordon identities, and parity questions
AU - Kim, Sun
AU - Yee, Ae Ja
N1 - Funding Information:
E-mail addresses: [email protected] (S. Kim), [email protected] (A.J. Yee). 1 The second author is partially supported by National Science Foundation Grant DMS-0801184 and by National Security Agency Grant H98230-10-1-0205.
PY - 2013/7
Y1 - 2013/7
N2 - Recently, George Andrews investigated a variety of parity questions in classical partition identities. In particular, he involved parity restrictions in the Rogers-Ramanujan-Gordon identities. In this paper, we reveal the relationship of his results with Bressoud's generalization of the Rogers-Ramanujan-Gordon identities. In addition, Andrews observed that one case of his identities is related to the Göllnitz-Gordon identities. In the light of the fact that the Göllnitz-Gordon identities are special cases of a general partition theorem of Andrews, we extend Andrews' identities by generalizing his observation. We also provide a generating function of the missing case of his identities.
AB - Recently, George Andrews investigated a variety of parity questions in classical partition identities. In particular, he involved parity restrictions in the Rogers-Ramanujan-Gordon identities. In this paper, we reveal the relationship of his results with Bressoud's generalization of the Rogers-Ramanujan-Gordon identities. In addition, Andrews observed that one case of his identities is related to the Göllnitz-Gordon identities. In the light of the fact that the Göllnitz-Gordon identities are special cases of a general partition theorem of Andrews, we extend Andrews' identities by generalizing his observation. We also provide a generating function of the missing case of his identities.
UR - http://www.scopus.com/inward/record.url?scp=84874401964&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874401964&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2013.02.005
DO - 10.1016/j.jcta.2013.02.005
M3 - Article
AN - SCOPUS:84874401964
SN - 0097-3165
VL - 120
SP - 1038
EP - 1056
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 5
ER -