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The phrase "a stack of assignments" is correct and usable in written English.
It can be used when referring to a large number of tasks or homework that need to be completed.
Example: "After returning from vacation, I was greeted by a stack of assignments waiting for me on my desk."
Alternatives: "a pile of assignments" or "a mountain of assignments".
Exact(1)
Instead, he must face a stack of assignments, and read and grade them on his own time.
Similar(59)
Stack valued assignments assign to each variable a stack of values, the top of the stack being the current value.
Despite her cheery countenance and assiduous completion of assignments, Ms. DeWitt had already bought razor blades and written a stack of goodbye letters to loved ones.
Inside is a stack of papers.
–A stack of blank CDs ($11).
Ah yes, a stack of lonely nights.
A stack of paper arrived.
On a stack of Penthouse Forums.
Rebin a stack of 2-dimensional images.
Average a stack of 26 images.
A stack of files may be used.
More suggestions(1)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com