A new approach for counting patterns in language theory, matchings, and set partitions

Fatima Hessas, Mouloud Goubi and Noria Benkhemmou

International Journal of Mathematics in Operational Research, 2025, vol. 32, issue 3, 426-442

Abstract: The notion of pattern is widely studied in the literature. We focus our attention on patterns appearing in language theory, matchings, and set partitions. We start with some main tools of algebraic generating functions of sequences of numbers. We explain how the Bell, Fibonacci and generalised Fibonacci numbers can be used in the theory of patterns. In particular, we are interested in words containing patterns that are related to arbitrary length so as to provide enumeration formulae, and extract satisfying recurrence relations. Moreover, we revisit the work of Bloom and Elizalde concerning pattern avoidance in matchings and partitions in order to fulfil it with some enumeration formulae.

Keywords: language theory; patterns; generating functions; matchings; set partitions. (search for similar items in EconPapers)
Date: 2025
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