  We report results of a numerical-relativity simulation for the merger of a
black hole-neutron star binary with a variety of equations of state (EOSs)
modeled by piecewise polytropes. We focus in particular on the dependence of
the gravitational waveform at the merger stage on the EOSs. The initial
conditions are computed in the moving-puncture framework, assuming that the
black hole is nonspinning and the neutron star has an irrotational velocity
field. For a small mass ratio of the binaries (e.g., MBH/MNS = 2 where MBH and
MNS are the masses of the black hole and neutron star, respectively), the
neutron star is tidally disrupted before it is swallowed by the black hole
irrespective of the EOS. Especially for less-compact neutron stars, the tidal
disruption occurs at a more distant orbit. The tidal disruption is reflected in
a cutoff frequency of the gravitational-wave spectrum, above which the spectrum
amplitude exponentially decreases. A clear relation is found between the cutoff
frequency of the gravitational-wave spectrum and the compactness of the neutron
star. This relation also depends weakly on the stiffness of the EOS in the core
region of the neutron star, suggesting that not only the compactness but also
the EOS at high density is reflected in gravitational waveforms. The mass of
the disk formed after the merger shows a similar correlation with the EOS,
whereas the spin of the remnant black hole depends primarily on the mass ratio
of the binary, and only weakly on the EOS. Properties of the remnant disks are
also analyzed.
