The N! conjecture is a mathematical hypothesis related to combinatorial structures, particularly focusing on permutations and certain types of combinatorial objects. More specifically, the conjecture proposes that for any integer \( N \), there exists a link between the factorial of \( N \) (denoted as \( N! \)) and certain countable properties of permutations or combinations of \( N \) items. One of the well-known formulations of the N!
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