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...huffle on trajectories was introduced by Mateescu, Rozenberg, and Salomaa [9] in order to generalize several operations on words and languages, and was investigated in detail by Domaratzki, e.g., see =-=[8]-=-. In this paper, we generalize orthogonal catenation to orthogonal shuffle on trajectories, and investigate several problems related to this operation. The paper is organized as follows. Section 2 con...

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...s We now consider deletion on trajectories, an important addition to the study of trajectories and related areas. The concept of deletion along trajectories was independently introduced by the author =-=[17, 22]-=- and Kari and Sosík [55, 56]. The primary motivation for the introduction of deletion on trajectories is to define an “inverse” to shuffle on trajectories, in a sense we will see below. Intuitively, d...

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...utative submonoid of a free monoid contains infinitely many primitive words [11]. In the literature, there are various types of generalizations/extensions of the classic definition of primitive words =-=[3, 4, 5, 7]-=-. We propose yet another generalization of primitive word, viz. L-primitive word – a nonempty word that is not a proper power of any word in a given language L. In this paper, we first investigate the...