The immersion poset on partitions

Lisa Johnston, David Kenepp, Evuilynn Nguyen +4

We introduce the immersion poset $(\mathcal{P}(n),{⩽}_I)$ on partitions, defined by $\hat{I}»{⩽}_I\hat{I}¼$ if and only if $s_{\hat{I}}¼(x_1,\dots ,x_N)-s_{\hat{I}}»(x_1,\dots ,x_N)$ is mo…