  We consider the factorization of permutations into bandwidth 1 permutations,
which are products of mutually nonadjacent simple transpositions. We exhibit an
upper bound on the minimal number of such factors and thus prove a conjecture
of Gilbert Strang: a banded permutation of bandwidth $w$ can be represented as
the product of at most $2w-1$ permutations of bandwidth 1. An analogous result
holds also for infinite and cyclically banded permutations.
