ScalingStacks

Example 3.2.10. The elements of $\hat{{\mathfrak{S}}}_{n}^{+}$ correspond to strand diagrams where the strands wind positively around the cylinder. The relation $c^{2}T_{n-1}=T_{1}c^{2}$ is illustrated below:

We describe some elements $w\in\hat{{\mathfrak{S}}}_{7}^{+}$ and the image of $T_{w}$ in $A_{7}$:

The element $(0,0,0,0,1,0,0)\in({\mathbf{Z}}_{\geq 0})^{7}$ corresponds to the following element of ${\mathfrak{S}}_{7}^{+}$: