On two unimodal descent polynomials. (English) Zbl 1392.05004
Summary: The descent polynomials of separable permutations and derangements are both demonstrated to be unimodal. Moreover, we prove that the \(\gamma\)-coefficients of the first are positive with an interpretation parallel to the classical Eulerian polynomial, while the second is spiral, a property stronger than unimodality. Furthermore, we conjecture that they are both real-rooted.
Keywords:
separable permutations; large Schröder numbers; derangements; \(\gamma\)-positive; spiral propertyReferences:
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