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Abstract We introduce the immersion poset$$({\mathcal {P}}(n), \leqslant _I)$$ $(P\left(n\right),{⩽}_I)$on partitions, defined by$$\lambda \leqslant _I \mu $$ $\lambda {⩽}_I\mu$if and only if$$s_\mu (x_1, \ldots , x_N) - s_\lambda (x_1, \ldots , x_N)$$ $s_{\mu }(x_1,\dots ,x_N)-s_{\lambda }(x_1,\dots ,x_N)$is monomial-positive. Relations in the immersion poset determine when irreducible polynomial representations of$$GL_N({\mathbb {C}})$$ $G{L}_N\left(C\right)$form an immersion pair, as defined by Prasad and Raghunathan [7]. We develop injections$$\textsf{SSYT}(\lambda , \nu ) \hookrightarrow \textsf{SSYT}(\mu , \nu )$$ $\mathrm{SSYT}(\lambda ,\nu )\hookrightarrow \mathrm{SSYT}(\mu ,\nu )$on semistandard Young tableaux given constraints on the shape of$$\lambda $$ $\lambda$, and present results on immersion relations among hook and two column partitions. The standard immersion poset$$({\mathcal {P}}(n), \leqslant _{std})$$ $(P\left(n\right),{⩽}_{\mathrm{std}})$is a refinement of the immersion poset, defined by$$\lambda \leqslant _{std} \mu $$ $\lambda {⩽}_{\mathrm{std}}\mu$if and only if$$\lambda \leqslant _D \mu $$ $\lambda {⩽}_D\mu$in dominance order and$$f^\lambda \leqslant f^\mu $$ $f^{\lambda }⩽f^{\mu }$, where$$f^\nu $$ $f^{\nu }$is the number of standard Young tableaux of shape$$\nu $$ $\nu$. We classify maximal elements of certain shapes in the standard immersion poset using the hook length formula. Finally, we prove Schur-positivity of power sum symmetric functions on conjectured lower intervals in the immersion poset, addressing questions posed by Sundaram [12]. 

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