A Survey of multipartitions: Congruences and identities

Research output: Chapter in Book/Report/Conference proceedingChapter

19 Citations (Scopus)

Abstract

The concept of a multipartition of a number, which has proved so useful in the study of Lie algebras, is studied for its own intrinsic interest. Following up on the work of Atkin, we shall present an infinite family of congruences for Pκ (n), the number of k-component multipartitions of n. We shall also examine the enigmatic tripentagonal number theorem and show that it implies a theorem about tripartitions. Building on this latter observation, we examine a variety of multipartition identities connecting them with mock theta functions and the Rogers-Ramanujan identities.

Original languageEnglish (US)
Title of host publicationSURVEYS IN NUMBER THEORY
EditorsKRISHNASWAMI ALLADI
Pages1-19
Number of pages19
DOIs
StatePublished - Dec 1 2008

Publication series

NameDevelopments in Mathematics
Volume17
ISSN (Print)1389-2177

Fingerprint

Congruence
Mock theta Functions
Rogers-Ramanujan Identities
Theorem
Lie Algebra
Imply
Observation
Family
Concepts

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Andrews, G. E. (2008). A Survey of multipartitions: Congruences and identities. In KRISHNASWAMI. ALLADI (Ed.), SURVEYS IN NUMBER THEORY (pp. 1-19). (Developments in Mathematics; Vol. 17). https://doi.org/10.1007/978-0-387-78510-3_1
Andrews, George E. / A Survey of multipartitions : Congruences and identities. SURVEYS IN NUMBER THEORY. editor / KRISHNASWAMI ALLADI. 2008. pp. 1-19 (Developments in Mathematics).
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Andrews, GE 2008, A Survey of multipartitions: Congruences and identities. in KRISHNASWAMI ALLADI (ed.), SURVEYS IN NUMBER THEORY. Developments in Mathematics, vol. 17, pp. 1-19. https://doi.org/10.1007/978-0-387-78510-3_1

A Survey of multipartitions : Congruences and identities. / Andrews, George E.

SURVEYS IN NUMBER THEORY. ed. / KRISHNASWAMI ALLADI. 2008. p. 1-19 (Developments in Mathematics; Vol. 17).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Andrews GE. A Survey of multipartitions: Congruences and identities. In ALLADI KRISHNASWAMI, editor, SURVEYS IN NUMBER THEORY. 2008. p. 1-19. (Developments in Mathematics). https://doi.org/10.1007/978-0-387-78510-3_1