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Real-rooted Eulerian polynomials from permutations, words, and paths
We study six Eulerian-type polynomial families. We prove that the descent polynomials of derangements are real-rooted, settling the derangement part of a conjecture of S.~Fu, Z.~Lin, and J.~Zeng. The proof uses a compatible-pair recursion and finite-symbol stability. We also resolve the real
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