# What does $b_i\mid b_{i+1}$ mean in this context?

In the computational topology literature, the reduction algorithm for computing the Smith normal form of a boundary matrix uses the notation $b_j > 1 \: \text{ and }\: b_j\mid b_{j+1}$ in the context of the diagonal elements of the Smith matrix. Can anyone give me an idea for what it means?

#### Solutions Collecting From Web of "What does $b_i\mid b_{i+1}$ mean in this context?"

The $b_i$ are integers and $|$ stands for “divides.”

-Qiaochu Yuan

Yes, it’s standard notation in this context.

-lhf