  We shall work with the so called duality triads following kwa\'sniewski. In
particular in this note we propose some extensions of them - hence we choose
such special class of triads that admit - all at once - a unified combinatorial
interpretation in a way konvalina does. The proposed extensions contain also
definition of operator valued arrays of konvalina-like coefficients - for the
sake of future investigation and applications.

Combinatorics