Do we need a grammar of irregular sequences

Combinations of a preposition and a singular count noun (P+Noun) occur with considerable frequency in German everyday speech. Yet it is unclear whether syntactic means, morphological opera-tions, or other processes should handle the combi-nation. If P+Noun combinations were analyzed as PPs, the grammar rule that handled singular count nouns and determiners would have to be amended. But a morphological analysis would require the formulation of a new word formation process, since P+Noun-formations are not known otherwise. It has thus been suggested that the combinations do not come about as result of an application of a rule of grammar, and perhaps that P+Noun combinations simply have to be listed. This assumption has been corroborated by the observation that the combina-tion is not free in the sense that any P may combine with any Noun, and that the construction is not transparent to competent speakers in the sense that they cannot produce new instances on the fly. This observation leads to the conjecture that the set of P+Noun may be large, yet finite, and hence should be treated as listemes instead of being subject to rule application. The present paper argues on the basis of statistical evidence that the set of P+Noun combinations is infinite, and hence that P+Noun must be handled by a rule of grammar, be it syntac-tic or morphological.