We present measurements of the production of D s − mesons relative to D s + mesons as functions of x F and of p t 2 for a sample of 2445 D s decays to φπ. The D s mesons were produced in Fermilab experiment E791 with 500 GeV/c π − mesons incident on one platinum and four carbon foil targets. The acceptance-corrected integrated asymmetry in the x F range −0.1 to 0.5 for D s ∓ mesons is 0.032 ± 0.022 ± 0.022, consistent with no net asymmetry. We compare the results as functions of x F and p t 2 to predictions and to the large production asymmetry observed for D ± mesons in the same experiment. These comparisons support the hypothesis that production asymmetries come from the fragmentation process and not from the charm quark production itself.2 Previous studies of charm particle production in hadron beams [1][2][3][4][5][6][7][8][9] have shown large enhancements in the forward production of charm particles that contain a quark or di-quark in common with the beam (leading particles) relative to those that do not (non-leading particles). Neither leading-order nor next-to-leading-order perturbative QCD calculations of charm quark production can account for the observed asymmetries [10,11]. The phenomenon is due either to unexpected contributions to charm quark production or to features of the hadronization process.Three classes of models have been proposed to account for hadronization in the beam fragmentation region: coalescence of produced charm quarks with valence quarks or diquarks from the beam [12][13][14], coalescence of charm and valence quarks when both originate in the beam particle [15][16][17], and string fragmentation as implemented in the Lund Model of the PYTHIA Monte Carlo program [18] and by Piskounova [19]. All these models involve a mechanism of attachment between the produced charm quarks and the valence quarks in the beam, and include a varying amount of actual coalescence. This coalescence is the dominant mechanism for the leading particle effect in the first two classes of models. They include no mechanism which will lead to a significant production asymmetry between particles except when one of them has a quark in common with the beam and the other does not. Since the probability of coalescence between two quarks is larger when they have similiar velocities, the production asymmetry between leading and nonleading charm mesons is expected to grow larger with increasing x F and smaller with increasing p t 2 . While D ± data from Fermilab experiment E791 do show the expected increase in asymmetry with increasing x F , they do not support the prediction of decreasing asymmetry withIn string fragmentation models, specifically the PYTHIA/LUND implementation, a produced charm quark is always initially connected via color strings to valence quarks or diquarks in the beam and the target. A leading particle can be produced by a meson beam in cases where the string attaches a charm quark to a beam antiquark and/or an anticharm quark to a beam quark. Some fraction of the time, the 3 string invaria...