  In this paper we perform a detailed study of the masses and mixing of the
single charmed scalar tetraquarks: $c q \bar{q} \bar{q}$. We also give a
systematic analysis of these tetraquark states by weight diagrams, quantum
numbers and flavor wave functions. Tetraquark masses are calculated using four
different fits. The following SU(3)$_\mathrm{F}$ representations are discussed:
$\bar{15}_\mathrm{S}$, $\bar{3}_\mathrm{S}$, $6_\mathrm{A}$ and
$\bar{3}_\mathrm{A}$. We use the flavor-spin Glozman-Riska interaction
Hamiltonian with SU(3) flavor symmetry breaking. There are 27 different
tetraquarks composed of a charm quark $c$ and of the three light flavors $u, d,
s$: 11 cryptoexotic (3 D$_\mathrm{s}^{+}$, 4 D$^{+}$, 4 D$^{0}$) and 16
explicit exotic states. We discuss D$_\mathrm{s}$ and its isospin partners in
the same multiplet, as well as all the other four-quark states. Some explicit
exotic states appear in the spectrum with the same masses as
D$_\mathrm{s}^{+}$(2632) in $\bar{15}_\mathrm{S}$ and with the same masses as
D$_\mathrm{s}^{+}$(2317) in $6_\mathrm{A}$ representation, which confirm the
tetraquark nature of these states.
