TY - CHAP
T1 - A Survey of multipartitions
T2 - Congruences and identities
AU - Andrews, George E.
PY - 2008
Y1 - 2008
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 -