Abstract
We study in this work properties of a combinatorial expansion of the classical Eulerian polynomial A n ( t ) , including the recurrence relation and the exponential generating function for the expansion coefficients. Analogous results for the Eulerian polynomials of types B and D are also obtained. The expansions obtained enable us to readily deduce the symmetry, unimodality, and alternating behavior at t = − 1 of the corresponding Eulerian polynomials, where the latter property settles the Charney–Davis conjecture for the Coxeter complexes of types A, B and D with combinatorial interpretations given to the corresponding Charney–Davis quantities.
Published Version
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