Context-Free Grammars for Several Polynomials Associated with Eulerian Polynomials

Shi-Mei Ma, Jun Ma, Yeong-Nan Yeh, Bao-Xuan Zhu

Abstract


In this paper, we present grammatical descriptions of several polynomials associated with Eulerian polynomials, including q-Eulerian polynomials, alternating run polynomials and derangement polynomials. As applications, we get several convolution formulas involving these polynomials.

Keywords


Eulerian polynomials; Alternating runs; Derangement polynomials; Context-free grammars

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