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.
Original languageEnglish
Pages (from-to)199-218
Number of pages20
JournalInternational Journal of Number Theory
Volume4
Issue number2
DOIs
StatePublished - 1 Apr 2008

ID: 126317340