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.

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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 -