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Partition representations: Difference between revisions
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Partition representations (view source)
Revision as of 15:29, 28 January 2020
, 15:29, 28 January 2020→Definitions: Partitions can't be empty
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== Definitions == | == Definitions == | ||
In this page, a '''partition''' of a [[vector]] is defined to be a [[nested]] or [[box]]ed vector containing vectors, such that the [[Raze]] (or equivalently <source lang=apl inline>{⊃⍪/⍵}</source> in [[Nested array model|nested]] APLs) of the partition intolerantly [[match]]es the original vector. A partition contains all the original [[element]]s of the vector, in the same order, but at one greater [[depth]]. | In this page, a '''partition''' of a [[vector]] is defined to be a non-[[empty]] [[nested]] or [[box]]ed vector containing vectors, such that the [[Raze]] (or equivalently <source lang=apl inline>{⊃⍪/⍵}</source> in [[Nested array model|nested]] APLs) of the partition intolerantly [[match]]es the original vector. A partition contains all the original [[element]]s of the vector, in the same order, but at one greater [[depth]]. | ||
The vectors contained in a partition are called '''divisions''', and the boundaries between them are called '''dividers'''. Although the English word "partition" can be used for either of these, the ambiguity of using one word for three different objects could be confusing. Only boundaries between divisions are called dividers: we do not name the two outermost edges, which must exist in any partition. | The vectors contained in a partition are called '''divisions''', and the boundaries between them are called '''dividers'''. Although the English word "partition" can be used for either of these, the ambiguity of using one word for three different objects could be confusing. Only boundaries between divisions are called dividers: we do not name the two outermost edges, which must exist in any partition. | ||