### PCP-prime words and primality types

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For a non-negative integer , we say that a language is if the number of words of length in is of order $\mathcal{O}\left({n}^{k}\right)$. We give a precise characterization of the -poly-slender context-free languages. The well-known characterization of the -poly-slender regular languages is an immediate consequence of ours.

In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix product gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting interconnection between mirror images of words and inverses of matrices.

In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix product gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting interconnection between mirror images of words and inverses of .

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