On two unimodal descent polynomials |
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| Authors: | Shishuo Fu Zhicong Lin Jiang Zeng |
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| Institution: | 1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China;2. School of Science, Jimei University, Xiamen 361021, PR China;3. CAMP, National Institute for Mathematical Sciences, Daejeon 305-811, Republic of Korea;4. Institut Camille Jordan, Université Claude Bernard Lyon 1, France |
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| Abstract: | The descent polynomials of separable permutations and derangements are both demonstrated to be unimodal. Moreover, we prove that the -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. |
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| Keywords: | Separable permutations Large Schröder numbers Derangements Spiral property |
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