  Measurements of the top quark-antiquark pair production cross section,
$\sigma_\mathrm{t\bar{t}}$, can be used to constrain the strong coupling
constant, $\alpha_{S}$, the top quark mass, $m_\mathrm{t}$, and the parton
distribution functions (PDFs). In this poster, the two most recent relevant
results published by the CMS Collaboration are presented. The analyses are
performed using proton-proton collision data at a centre-of-mass energy of 13
TeV recorded by the CMS detector at the CERN LHC in 2016, corresponding to an
integrated luminosity of $35.9~\mathrm{fb^{-1}}$. In the first one,
$\alpha_{S}$ and $m_\mathrm{t}$ are extracted independently from a measurement
of the inclusive $\sigma_\mathrm{t\bar{t}}$, using next-to-next-to-leading
order theoretical predictions. In the second, a measurement of the normalized
triple-differential $\mathrm{t\bar{t}}$ cross section is performed; the result
is then used together with HERA deep-inelastic scattering data to perform a
simultaneous determination of $\alpha_{S}$, $m_\mathrm{t}$, and the PDFs, at
next-to-leading order. As a result, the uncertainty in the gluon PDF and its
correlation with $\alpha_{S}$ are significantly reduced at high parton momentum
fraction, the kinematic range probed by $\mathrm{t\bar{t}}$ production. The
result also yields the most precise determination of the top quark pole mass,
to date.
