Advances and Applications in Discrete Mathematics
Volume 29, Issue 2, Pages 139 - 154
(February 2022) http://dx.doi.org/10.17654/0974165822010 |
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SEPARATION NUMBERS WITH RESPECT TO SQUARE NUMBERS
Wonhong Lee and Sang-Mok Kim
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Abstract: A partially ordered set is ‘top r separable’ if its ground set can be partitioned as so that for all and all with For a given n-set, the minimum number of k-subsets whose transitive closure of chains on each subsets is top r-separable, denoted by is called the separation number of and r. In this paper, we first give some basic properties of and obtain that and Next, we prove that and if In addition, this result can be seen as in terms of triangular number of order a natural number r.
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Keywords and phrases: finite ordered set, transitive closure, separability |
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