  We count the number of histories between the two degenerate minimum energy
configurations of the Ising model on a chain, as a function of the length n and
the number d of kinks that appear above the critical temperature. This is
equivalent to count permutations of length n avoiding certain subsequences
depending on d. We give explicit generating functions and compute the
asymptotics. The setting considered has a role when describing dynamics induced
by quantum Hamiltonians with deconfined quasi-particles.
