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Partitions of a 4-element set ordered by refinement. A partition α of a set X is a refinement of a partition ρ of X—and we say that α is finer than ρ and that ρ is coarser than α—if every element of α is a subset of some element of ρ. Informally, this means that α is a further fragmentation of ρ. In that case, it is written that ...
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are partition of a set or an ordered partition of a set,
Storing objects in a space-partitioning data structure (k-d tree or BSP tree for example) makes it easy and fast to perform certain kinds of geometry queries—for example in determining whether a ray intersects an object, space partitioning can reduce the number of intersection test to just a few per primary ray, yielding a logarithmic time ...
In computer science, binary space partitioning (BSP) is a method for space partitioning which recursively subdivides a Euclidean space into two convex sets by using hyperplanes as partitions. This process of subdividing gives rise to a representation of objects within the space in the form of a tree data structure known as a BSP tree .
The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for
In materials science, segregation is the enrichment of atoms, ions, or molecules at a microscopic region in a materials system. While the terms segregation and adsorption are essentially synonymous, in practice, segregation is often used to describe the partitioning of molecular constituents to defects from solid solutions, [1] whereas adsorption is generally used to describe such partitioning ...
Among the 22 partitions of the number 8, there are 6 that contain only odd parts: 7 + 1; 5 + 3; 5 + 1 + 1 + 1; 3 + 3 + 1 + 1; 3 + 1 + 1 + 1 + 1 + 1; 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1; Alternatively, we could count partitions in which no number occurs more than once. Such a partition is called a partition with distinct parts. If we count the ...
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2.