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.
Charged particles ($h^\pm$) and \kz mesons have been studied in photoproduced events containing at least one jet of $E_T > 8$ GeV in a pseudorapidity interval (--0.5, 0.5) in the ZEUS laboratory frame. Distributions are presented in terms of transverse momentum, pseudorapidity and distance of the particle from the axis of a jet. The properties of \hpm within the jet are described well using the standard settings of PYTHIA, but the use of the multiparton interaction option improves the description outside the jets. A reasonable overall description of the \kz behaviour is possible with PYTHIA using a reduced value of the strangeness suppression parameter. The numbers of $h^\pm$ and \kz within a jet as defined above are measured to be $3.25\pm0.02\pm0.28$ and $0.431\pm0.013\pm0.088$ respectively. Fragmentation functions are presented for $h^\pm$ and \kz in photoproduced jets; agreement is found with calculations of Binnewies et al. and, at higher momenta, with $p\bar p$ scattering and with standard PYTHIA. Fragmentation functions in direct photoproduced events are extracted, and at higher momenta give good agreement with data from related processes in $e^+e^-$ annihilation and deep inelastic $ep$ scattering.