The notion of reversibility  in algebras for generalized
Pascal triangles and local rules of one-dimensional cellular
automata is discussed. Several constructions of such
algebras and rules are presented. Some constructions start
from operations satisfying cancellation law and produce
reversible operations, resp. local rules. Other
constructions, permutation of values and permutation of
arguments, (1)~preserve reversibility and (2)~give
nontrivial examples from simpler ones. These constructions
are very simple but nevertheless they can substantially
increase the complexity of underlying generalized Pascal
triangles (or computations of cellular automata).
