2022
DOI: 10.48550/arxiv.2204.01497
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The Dumont Ansatz for the Eulerian Polynomials, Peak Polynomials and Derivative Polynomials

Abstract: We observe that three context-free grammars of Dumont can be brought to a common ground, via the idea of transformations of grammars, proposed by Ma-Ma-Yeh. Then we develop a unified perspective to investigate several combinatorial objects in connection with the bivariate Eulerian polynomials. We call this approach the Dumont ansatz. As applications, we provide grammatical treatments, in the spirit of the symbolic method, of relations on the Springer numbers, the Euler numbers, the three kinds of peak polynomi… Show more

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