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In this paper, we study the desingularization problem in the first q -Weyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q -Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q -Weyl closure of a given q -difference operator. As an application, we certify that several instances of the colored Jones polynomial are Laurent polynomial sequences by computing the corresponding desingularized operator. [ABSTRACT FROM AUTHOR]

Abstract: The gap function of an infinite word over the binary alphabet gives the distances between consecutive 1''s in this word. In this paper we study infinite binary words whose gap function is injective or “almost injective.” A method for computing the subword complexity of such words is given. A necessary and sufficient condition for a function to be the subword complexity function of a binary word whose gap function is increasing is obtained. [Copyright &y& Elsevier]