  By removing one empty site between two occupied sites, we map the ground
states of chains of hardcore bosons and spinless fermions with infinite
nearest-neighbor repulsion to ground states of chains of hardcore bosons and
spinless fermions without nearest-neighbor repulsion respectively, and
ultimately in terms of the one-dimensional Fermi sea. We then introduce the
intervening-particle expansion, where we write correlation functions in such
ground states as a systematic sum over conditional expectations, each of which
can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various
ground-state correlation functions are calculated for the bosonic and fermionic
chains with infinite nearest-neighbor repulsion, as well as for a ladder model
of spinless fermions with infinite nearest-neighbor repulsion and correlated
hopping in three limiting cases. We find that the decay of these correlation
functions are governed by surprising power-law exponents.
