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The American Mathematical Monthly Volume 125, 2018 - Issue 5
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Notes

Set Partitions with Isolated Singletons

Augustine O. MunagiSchool of Mathematics, University of the Witwatersrand, 2050Johannesburg, South [email protected]
Pages 447-452 | Published online: 12 Apr 2018
 
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Abstract

We give results for partitions of the set of the first n natural numbers into k nonempty subsets S1, S2, …, Sk with respect to the number of isolated elements, that is, with respect to integers a such that if a belongs to Si, then neither a − 1 nor a + 1 belongs to Si.

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