The Rogers-Ramanujan-Gordon identities, the generalized Göllnitz-Gordon identities, and parity questions

Sun Kim, Ae Ja Yee

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1038-1056
Number of pages19
JournalJournal of Combinatorial Theory. Series A
Volume120
Issue number5
DOIs
StatePublished - Jul 1 2013

Fingerprint

Ramanujan
Parity
Partition Identities
Generating Function
Partition
Restriction
Theorem

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

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abstract = "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 G{\"o}llnitz-Gordon identities. In the light of the fact that the G{\"o}llnitz-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.",
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The Rogers-Ramanujan-Gordon identities, the generalized Göllnitz-Gordon identities, and parity questions. / Kim, Sun; Yee, Ae Ja.

In: Journal of Combinatorial Theory. Series A, Vol. 120, No. 5, 01.07.2013, p. 1038-1056.

Research output: Contribution to journalArticle

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