Contact formulas for rational plane curves via stable maps

Extending techniques of [4], we use stable maps, and their stable lifts to the Semple bundle variety of second-order curvilinear data, to calculate ce rtain characteristic numbers for rational plane curves. These characteristi c numbers involve first-order (tangency) and second-order (inflectional) co nditions. Although they may be virtual, they may be used as inputs in an en umeratively significant formula for the number of rational curves having a triple contact with a specified plane curve and passing through 3d - 3 gene ral points.