  The inclusive $b \bar{b}$- and $c \bar{c}$-dijet production cross-sections in
the forward region of $pp$ collisions are measured using a data sample
collected with the LHCb detector at a centre-of-mass energy of 13 TeV in 2016.
The data sample corresponds to an integrated luminosity of 1.6 fb$^{-1}$.
Differential cross-sections are measured as a function of the transverse
momentum and of the pseudorapidity of the leading jet, of the rapidity
difference between the jets, and of the dijet invariant mass. A fiducial region
for the measurement is defined by requiring that the two jets originating from
the two $b$ or $c$ quarks are emitted with transverse momentum greater than 20
GeV$/c$, pseudorapidity in the range $2.2 < \eta < 4.2$, and with a difference
in the azimuthal angle between the two jets greater than 1.5. The integrated $b
\bar{b}$-dijet cross-section is measured to be $53.0 \pm 9.7$ nb, and the total
$c \bar{c}$-dijet cross-section is measured to be $73 \pm 16$ nb. The ratio
between $c \bar{c}$- and $b \bar{b}$-dijet cross-sections is also measured and
found to be $1.37 \pm 0.27$. The results are in agreement with theoretical
predictions at next-to-leading order.
