A combinatorial correspondence related to Göllnitz’ (big) partition theorem and applications-Reference-Cited by-同舟云学术

A combinatorial correspondence related to Göllnitz’ (big) partition theorem and applications

Published:1997 Issue:7 Volume:349 Page:2721-2735
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Alladi Krishnaswami

Abstract

In recent work, Alladi, Andrews and Gordon discovered a key identity which captures several fundamental theorems in partition theory. In this paper we construct a combinatorial bijection which explains this key identity. This immediately leads to a better understanding of a deep theorem of Göllnitz, as well as Jacobi’s triple product identity and Schur’s partition theorem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1997-349-07/S0002-9947-97-01944-2/S0002-9947-97-01944-2.pdf

Reference11 articles.

1. K. Alladi, Partition identities involving gaps and weights, Trans. Amer. Math. Soc. (to appear).

2. K. Alladi, and G. E. Andrews, A new key identity for Göllnitz’ (big) partition theorem in Proc. 10^{𝑡ℎ} Anniv. Conf. Ramanujan Math. Soc., Contemp. Math. (to appear).

3. Generalizations and refinements of a partition theorem of Göllnitz;Alladi, Krishnaswami;J. Reine Angew. Math.,1995

4. Generalizations of Schur’s partition theorem;Alladi, Krishnaswami;Manuscripta Math.,1993

5. On a partition theorem of Göllnitz and related formulae;Andrews, George E.;J. Reine Angew. Math.,1969

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