  We study boson-fermion dualities in one-dimensional many-body problems of
identical particles interacting only through two-body contacts. By using the
path-integral formalism as well as the configuration-space approach to
indistinguishable particles, we find a generalization of the boson-fermion
duality between the Lieb-Liniger model and the Cheon-Shigehara model. We
present an explicit construction of $n$-boson and $n$-fermion models which are
dual to each other and characterized by $n-1$ distinct (coordinate-dependent)
coupling constants. These models enjoy the spectral equivalence, the
boson-fermion mapping, and the strong-weak duality. We also discuss a
scale-invariant generalization of the boson-fermion duality.
