Alternating Eulerian polynomials and left peak polynomials |
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| Institution: | 1. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Hebei 066004, PR China;2. Department of Mathematics, Northeastern University, Shenyang 110004, PR China;3. Department of Mathematics, University of Haifa, 3498838 Haifa, Israel;4. College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, PR China |
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| Abstract: | We first present grammatical interpretations for the alternating Eulerian polynomials of types A and B. As applications, we then derive several properties of the type B alternating Eulerian polynomials, including recurrence relations, generating function and unimodality. And then, we establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials, which implies that the type B alternating Eulerian polynomials have gamma-vectors that alternate in sign. |
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| Keywords: | Eulerian polynomials Alternating descents Left peaks Gamma-vectors |
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