  Theoretical models of very metal-poor intermediate-mass Asymptotic Giant
Branch (AGB) stars predict a large overabundance of primary nitrogen. The very
metal-poor, carbon-enhanced, s-process-rich stars, which are thought to be the
polluted companions of now-extinct AGB stars, provide direct tests of the
predictions of these models. Recent studies of the carbon and nitrogen
abundances in metal-poor stars have focused on the most carbon-rich stars,
leading to a potential selection bias against stars that have been polluted by
AGB stars that produced large amounts of nitrogen, and hence have small [C/N]
ratios. We call these stars Nitrogen-Enhanced Metal-Poor (NEMP) stars, and
define them as having [N/Fe] > +0.5 and [C/N] < -0.5. In this paper, we report
on the [C/N] abundances of a sample of 21 carbon-enhanced stars, all but three
of which have [C/Fe] < +2.0. If NEMP stars were made as easily as
Carbon-Enhanced Metal-Poor (CEMP) stars, then we expected to find between two
and seven NEMP stars. Instead, we found no NEMP stars in our sample. Therefore,
this observational bias is not an important contributor to the apparent dearth
of N-rich stars. Our [C/N] values are in the same range as values reported
previously in the literature (-0.5 to +2.0), and all stars are in disagreement
with the predicted [C/N] ratios for both low-mass and high-mass AGB stars. We
suggest that the decrease in [C/N] from the low-mass AGB models is due to
enhanced extra-mixing, while the lack of NEMP stars may be caused by
unfavorable mass ratios in binaries or the difficulty of mass transfer in
binary systems with large mass ratios.
