On the Broken 1-diamond Partition
نویسنده
چکیده
Abstract. 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.
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