Abstract:
We consider some partition polynomials such that partial Bell and Platonov
polynomials, generalised $A$- and $B$-polynomials, Touchard $T$- and $C$-polynomials,
and $P$-polynomials which compose a quasi-orthogonal system
with $T$-polynomials. We investigate the properties of the
coefficients of these polynomials, present recurrence relations and
combinatorial interpretations.
For $C$-polynomials, we give recurrence relations,
generating functions, and explicit expressions.