  We study the properties of a quantum dot coupled to a one-dimensional
topological superconductor and a normal lead and discuss the interplay between
Kondo and Majorana-induced couplings in quantum dot. The latter appears due to
the presence of Majorana zero-energy modes localized at the ends of the
one-dimensional superconductor. We investigate the phase diagram of the system
as a function of Kondo and Majorana interactions using a renormalization-group
analysis, a slave-boson mean-field theory and numerical simulations using the
density-matrix renormalization group method. We show that, in addition to the
well-known Kondo fixed point, the system may flow to a new fixed point
controlled by the Majorana-induced coupling which is characterized by
non-trivial correlations between a localized spin on the dot and the fermion
parity of the topological superconductor and normal lead. We compute several
measurable quantities such as differential tunneling conductance and impurity
spin susceptibility which highlight some peculiar features characteristic to
the Majorana fixed point.
