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Combinatorial proof demonstrates log-convexity of derangements in permutations, indicating structured properties in combinatorial mathematics.
We provide a combinatorial proof for the fact that the numbers of derangements of length n form a log-convex sequence for n≥3. A minor modification of our proof yields the same result for permutations of length n≥4 that have exactly one fixed point. We explain why these statements do not generalize for permutations with exactly k fixed points where k≥3.
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Miklós Bóna (2026) studied this question.
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