  The first measurement of inclusive Ds+- photoproduction at HERA has been
performed with the ZEUS detector for photon-proton centre-of-mass energies 130
< W < 280 GeV. The measured cross section for 3 < pt(Ds) < 12 GeV and
|eta(Ds)|< 1.5 is sigma(ep -> Ds X) = 3.79 +- 0.59 (stat.) +0.26-0.46 (syst.)
+- 0.94 (br.) nb, where the last error arises from the uncertainty in the Ds
decay branching ratio. The measurements are compared with inclusive D*+-
photoproduction cross sections in the same kinematic region and with QCD
calculations. The Ds cross sections lie above a fixed-order next-to-leading
order calculation and agree better with a tree-level O(alpha,alpha_s^3)
calculation that was tuned to describe the ZEUS D* cross sections. The ratio of
Ds+- to D*+- cross sections is 0.41 +- 0.07 (stat.) +0.03-0.05 (syst.) +- 0.10
(br.). From this ratio, the strangeness-suppression factor in charm
photoproduction, within the LUND string fragmentation model, has been
calculated to be gamma_s = 0.27 +- 0.05 +- 0.07 (br.). The cross-section ratio
and gamma_s are in good agreement with those obtained in charm production in
e+e- annihilation.
