In
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...
, a laminar set family is a
set family in which each pair of sets are either
disjoint or related by containment.
Formally, a set family is called laminar if for every ''i'', ''j'', the intersection of ''S
i'' and ''S
j'' is either empty, or equals ''S
i'', or equals ''S
j''.
Let ''E'' be a ground-set of elements. A laminar set-family on ''E'' can be constructed by recursively
partitioning ''E'' into parts and sub-parts. In particular, the
singleton family is laminar; if we partition ''E'' into some ''k'' pairwise-disjoint parts ''E''
1,...,''E
k'', then is laminar too; if we now partition e.g. ''E''
1 into ''E''
11, ''E''
12, ''... E''
1j, then adding these sub-parts yields another laminar family; etc. Hence, a laminar set-family can be seen as a partitioning of the ground-set into categories and sub-categories.
References
Families of sets
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