ScalingStacks

Example 3.2.8. An element $T_{\sigma}$ of $\hat{H}_{n}$ will be representated by a good strand diagram for $\sigma$. The multiplication of $T_{\sigma}$ and $T_{\sigma^{\prime}}$ is obtained by concatenating the diagrams of $\sigma$ and $\sigma^{\prime}$ (as in the multiplication of $\sigma$ and $\sigma^{\prime}$). If the corresponding diagram is good, then $T_{\sigma}T_{\sigma^{\prime}}=T_{\sigma^{\prime\prime}}$, where $\sigma^{\prime\prime}$ is represented by the concatenated diagram. Otherwise, $T_{\sigma}T_{\sigma^{\prime}}=0$. For example: