Browsing by Author "Hessas, Fatima"

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    On Generating function associated to patterns
    (UNIVERSITE´MOULOUD MAMMERI DE TIZI–OUZOU, 2024) Hessas, Fatima
    The notion of pattern is widely studied in the literature. In this paper we focus our attention on patterns appearing in language theory, perfect matchings and set partitions. Algebraic generating functions of sequences of numbers are the main tools used in our contribution. We explain how the Bell, Fibonacci, and generalised Fibonacci numbers and polynomials can be used in the theory of patterns that provide enumeration formulae. In the first part of our work we are interested in the enumeration of words of arbitrary length containing patterns from a finite alphabet. Recurrence relations and explicit formulae are extracted and proposed. Furthermore, we revisit the work of Bloom and Elizalde on the enumeration of pattern avoidance in perfect matchings and partitions in order to complete it with some recurrence relations and explicite formulae.
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    ON GENERATING FUNCTIONS ASSOCIATED TO PATTERNS
    (UNIVERSITE´MOULOUD MAMMERI de TIZI–OUZOU, 2024) Hessas, Fatima
    The notion of pattern is widely studied in the literature. In this paper we focus our attention on patterns appearing in language theory, perfect matchings and set partitions. Algebraic generating functions of sequences of numbers are the main tools used in our contribution. We explain how the Bell, Fibonacci, and generalised Fibonacci numbers and polynomials can be used in the theory of patterns that provide enumeration formulae. In the first part of our work we are interested in the enumeration of words of arbitrary length containing patterns from a finite alphabet. Recurrence relations and explicit formulae are extracted and proposed. Furthermore, we revisit the work of Bloom and Elizalde on the enumeration of pattern avoidance in perfect matchings and partitions in order to complete it with some recurrence relations and explicite formulae.