Set partitions with circular successions
نویسندگان
چکیده
We consider the enumeration of partitions of a finite set according to the number of consecutive elements inside a block under the assumption that the elements are arranged around a circle. This statistic, commonly known as circular succession, continues to play a significant role in many combinatorial problems involving combinations of a set following its first appearance in a paper of Irving Kaplansky in the 1940s. In this paper we obtain interesting formulas for the number of partitions avoiding a circular succession and the number of partitions containing a specified number of circular successions. Our methods include both elementary combinatorial reasoning and the application of ordinary and exponential power series generating functions. Several new combinatorial identities are also stated.
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عنوان ژورنال:
- Eur. J. Comb.
دوره 42 شماره
صفحات -
تاریخ انتشار 2014