  Schinzel's original problem was to describe when an expression f(x)-g(y),
with f,g nonconstant and having complex coefficients, is reducible. We call
such an (f,g) a Schinzel pair if this happens nontrivially: f(x)-g(y) is newly
reducible. Fried accomplished this as a special case of a result in
"http://www.math.uci.edu/~mfried/paplist-ff/dav-red.pdf">dav-red.pdf, when f is
indecomposable. That work featured using primitive permutation representations.
Even after 42 years going beyond using primitivity is a challenge to the
monodromy method despite many intervening related papers (see
http://www.math.uci.edu/~mfried/paplist-ff/UMStory.pdf">UMStory.pdf. Here we
develop a formula for branch cycles that characterizes Schinzel pairs
satisfying a condition of Avanzi, Gusic and Zannier and relate it to this
ongoing story.
