So I need to write a short story for my university writing portfolio and I was wondering if I could put a poem in it or would that be inappropriate for a short story? And are there any short stories out there that have poems in them?
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There are no "rules" for fiction, and appropriateness depends on whether it achieves the effect in the story you want it to.
There are many examples of novels which include poems/songs/lyrics (think Tolkien, Milne, Lewis Carroll), but I can't think of any short fiction that does so (though I am sure there must be examples.