In this paper we introduce the notion of generalized factorization for an arbitrary submonoid M subset of A*, where A* is the free monoid generated by an alphabet A, generalizing, in this way, the notion of factorization of A*. Then we give a characterization of the free product of two submonoids of A* in terms of unambiguous products of monoids. To do this we make use of the notion of coding partition of a set X subset of A(+), where A+ is the free semigroup generated by an alphabet A. Moreover, given a coding partition of a set X subset of A(+), we will show how to construct a generalized factorization of X *.
Burderi, F. (2025). Factorizations and Monoids. In Combinatorics on Words 15th International Conference, WORDS 2025 Nancy, France, June 30 – July 4, 2025 Proceedings (pp. 49-60). SPRINGER INTERNATIONAL PUBLISHING AG [10.1007/978-3-031-97548-6_5].
Factorizations and Monoids
Burderi F.
Primo
2025-06-30
Abstract
In this paper we introduce the notion of generalized factorization for an arbitrary submonoid M subset of A*, where A* is the free monoid generated by an alphabet A, generalizing, in this way, the notion of factorization of A*. Then we give a characterization of the free product of two submonoids of A* in terms of unambiguous products of monoids. To do this we make use of the notion of coding partition of a set X subset of A(+), where A+ is the free semigroup generated by an alphabet A. Moreover, given a coding partition of a set X subset of A(+), we will show how to construct a generalized factorization of X *.
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