### 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 language | English (US) |
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Title of host publication | SURVEYS IN NUMBER THEORY |

Editors | KRISHNASWAMI ALLADI |

Pages | 1-19 |

Number of pages | 19 |

DOIs | |

State | Published - Dec 1 2008 |

### Publication series

Name | Developments in Mathematics |
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Volume | 17 |

ISSN (Print) | 1389-2177 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*SURVEYS IN NUMBER THEORY*(pp. 1-19). (Developments in Mathematics; Vol. 17). https://doi.org/10.1007/978-0-387-78510-3_1

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - A Survey of multipartitions

T2 - Congruences and identities

AU - Andrews, George E.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84859500322&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859500322&partnerID=8YFLogxK

U2 - 10.1007/978-0-387-78510-3_1

DO - 10.1007/978-0-387-78510-3_1

M3 - Chapter

AN - SCOPUS:84859500322

SN - 9780387785097

T3 - Developments in Mathematics

SP - 1

EP - 19

BT - SURVEYS IN NUMBER THEORY

A2 - ALLADI, KRISHNASWAMI

ER -