Why does this paper use 1/cm for units of frequency? Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency.
Here is an excerpt:

It doesn't seem like wave number, as they clearly call it frequency. What's going on here?
$^*$ Sievers III, A. J., and M. Tinkham. "Far infrared antiferromagnetic resonance in MnO and NiO." Physical Review 129.4 (1963): 1566.
 A: People working in the infrared or optical region tend to sometimes, depending on what school of thought they come from, use a unit called wavenumber, which is the reciprocal wavelength in centimeters, $\frac{1}{\lambda_{centimeter}}$.
This is still a frequency, but instead of oscillations per second, it is oscillations per centimeter. 
This unit is also called a Kayser. Wavenumber and Kayser are commonly used when working with spectroscopy/diffraction. 
A: A frequency is a number of oscillations, but you need to specify the unit you're refering to : is it oscillations per a given duration (temporal frequency) or per a given length (spatial frequency). Today "frequency" implies a temporal frequency, and we use the word "wave number" for the spatial frequency, allowing us to go away with the adjective. That was not always the case.
A: Sometimes physicists use (lenghts)$^{-1}$ to indicate frequencies, expecially in spectroscopy...
As you well now, $\omega = 2\pi \nu$ and $c = \lambda \nu$ so that
$\omega = 2\pi \frac{c}{\lambda}$ which is proportional to $ \lambda ^ {-1},$ since $c$ is a constant. 
So when one says $\omega_1 = 29 cm^{-1}$ is actually saying $\omega_1 = c_{cgs}29 s^{-1} $ where $c_{cgs}$ is the speed of light in the cgs system
A: If you suppose c=1, then 'centimetre' is the time it takes for light to cross a centimetre, and a count of cycles per centimetre is something that can be done in nature, and also relates to the frequency in cycles per second.
