  In this paper we consider the gamma-vectors of the types A and B Coxeter
complexes as well as the gamma-vectors of the types A and B associahedrons. We
show that these gamma-vectors can be obtained by using derivative polynomials
of the tangent and secant functions. A grammatical description for these
gamma-vectors is discussed. Moreover, we also present a grammatical description
for the well known Legendre polynomials and Chebyshev polynomials of both
kinds.
