TY - JOUR

T1 - On the broken 1-diamond partition

AU - Mortenson, Eric

PY - 2008/4/1

Y1 - 2008/4/1

N2 - We introduce a crank-like statistic for a different class of partitions. In [AP], Andrews and Paule initiated the study of broken k-diamond partitions. Their study of the respective generating functions led to an infinite family of modular forms, about which they were able to produce interesting arithmetic theorems and conjectures for the related partition functions. Here we establish a crank-like statistic for the broken 1-diamond partition and discuss its role in congruence properties.

AB - We introduce a crank-like statistic for a different class of partitions. In [AP], Andrews and Paule initiated the study of broken k-diamond partitions. Their study of the respective generating functions led to an infinite family of modular forms, about which they were able to produce interesting arithmetic theorems and conjectures for the related partition functions. Here we establish a crank-like statistic for the broken 1-diamond partition and discuss its role in congruence properties.

UR - http://www.scopus.com/inward/record.url?scp=84877660567&partnerID=8YFLogxK

U2 - 10.1142/s1793042108001365

DO - 10.1142/s1793042108001365

M3 - Article

AN - SCOPUS:84877660567

VL - 4

SP - 199

EP - 218

JO - International Journal of Number Theory

JF - International Journal of Number Theory

SN - 1793-0421

IS - 2

ER -