  We present a detailed theory of transport through line junctions formed by
counterpropagating single-branch fractional-quantum-Hall edge channels having
different filling factors. Intriguing transport properties are exhibited when
strong Coulomb interactions between electrons from the two edges are present.
Such strongly correlated line junctions can be classified according to the
value of an effective line-junction filling factor n that is the inverse of an
even integer. Interactions turn out to affect transport most importantly for
n=1/2 and n=1/4. A particularly interesting case is n=1/4 corresponding to,
e.g., a junction of edge channels having filling factor 1 and 1/5,
respectively. We predict its differential tunneling conductance to oscillate as
a function of voltage. This behavior directly reflects the existence of novel
Majorana-fermion quasiparticle excitations in this type of line junction.
Experimental accessibility of such systems in current cleaved-edge overgrown
samples enables direct testing of our theoretical predictions.
