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- W1978450021 abstract "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." @default.
- W1978450021 created "2016-06-24" @default.
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- W1978450021 date "2014-11-01" @default.
- W1978450021 modified "2023-09-27" @default.
- W1978450021 title "Set partitions with circular successions" @default.
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- W1978450021 doi "https://doi.org/10.1016/j.ejc.2014.06.008" @default.
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