**N. Alon and W. Maass**

The notion of a *meander* is introduced and studied. Roughly speaking, a
meander is a sequence of integers (drawn from the set
) that wanders back and forth between various subsets of *a
lot*. Using Ramsey theoretic proof techniques we obtain sharp lower bounds on
the minimum length of meanders that achieve various levels of wandering. We
then apply these bounds to improve existing lower bounds on the length of
constant width *branching programs* for various symmetric functions. In
particular, an
lower bound on the length of any such
program for the majority function of bits is proved. We further obtain
optimal time-space trade-offs for certain input oblivious branching programs
and establish sharp lower bounds on the size of *weak
superconcentrators* of depth 2.