Open AccessOn the greatest distance between two partitions of the finite set
Author(s) -
S. V. Dronov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1791/1/012071
Subject(s) - disjoint sets , partition (number theory) , mathematics , finite set , value (mathematics) , combinatorics , discrete mathematics , statistics , mathematical analysis
Consider the family Ξ of all possible partitions of a given finite set into disjoint parts. Suppose we have A ∈ Ξ, and there is reason to consider this partition basic from a certain point of view. The greatest value d *( A ) of the special cluster metric d ( A, B ) is found, which is reached when its second argument runs through all B ∈ Ξ. The value of d *( A ) turns out to depend on the structure of the basic partition A. Using the found value of d *( A ), we propose a numerical coefficient whose value allows us to estimate the degree of difference between the basic partition and the newly built one. Such an assessment can help us to make a decision about the possibility of using the new partition instead of the basic one.