Singleton free set partitions avoiding a 3-element set
نویسنده
چکیده
The definition and study of pattern avoidance for set partitions, which is an analogue of pattern avoidance for permutations, begun with Klazar. Sagan continued his work by considering set partitions which avoids a single partition of three elements, and Goyt generalized these results by considering partitions which avoids any family of partitions of a 3-element set. In this paper we enumerate and describe set partitions, even set partitions and odd set partitions without singletons which avoids any family of partitions of a 3-element set. The characterizations of these families allows us to conclude that the corresponding sequences are P recursive. We also construct Gray codes for the sets of singletons free partitions that avoids a single partition of three elements.
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تاریخ انتشار 2013