Abstract
A multiplicative integer subshift $$X_\Omega $$ derived from the subshift $$\Omega $$ is invariant under multiplicative integer action, which is closely related to the level set of multiple ergodic average. The complexity of $$X_{\Omega }$$ is usually measured by entropy (or box dimension). This work concerns on two types of multi-dimensional multiplicative integer subshifts (MMIS) with different coupling constraints, and then obtains their entropy formulae.
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