Wikipedia:Category combinatorics

This page illustrates how some categories of articles can be categorized in larger categories by means of combinatorics, binomial expansion, and Pascal's triangle. The section "One factor" is included for continuation of the pattern.

The pattern can be complicated by intermediate categories with names having phrases such as "by nationality" (or "by country"), "by religious status", "by sex", "by occupation", "by employment status", and "by marital status".

The guidelines at Wikipedia:Category names might not apply universal consistency to the order of elements in category names.

One element in a category name

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  • Combination (1) of 1 element
X: Category:Scientists
  • Combination (1) of 0 element
_: Category:Contents
  • 1 + 1 = 2

Two elements in a category name

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  • Combination (1) of 2 elements
XX: Category:American scientists
  • Combinations (2) of 1 element
X_: Category:Americans
_X: Category:Scientists
  • Combination (1) of 0 element
__: Category:Contents
  • 1 + 2 + 1 = 4 = 2 × 2

Three elements in a category name

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  • Combination (1) of 3 elements
XXX: Category:American women scientists
  • Combinations (3) of 2 elements
XX_: Category:American women
X_X: Category:American scientists
_XX: Category:Women scientists
  • Combinations (3) of 1 element
X__: Category:Americans
_X_: Category:Women
__X: Category:Scientists
  • Combination (1) of 0 element
___: Category:Contents
  • 1 + 3 + 3 + 1 = 8 = 2 × 2 × 2

Four elements in a category name

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  • Combination (1) of 4 elements
XXXX: Category:American Jewish women scientists
  • Combinations (4) of 3 elements
XXX_: Category:American Jewish women
XX_X: Category:American Jewish scientists
X_XX: Category:American women scientists
_XXX: Category:Jewish women scientists
  • Combinations (6) of 2 elements
XX__: Category:American Jews
X_X_: Category:American women
X__X: Category:American scientists
_XX_: Category:Jewish women
_X_X: Category:Jewish scientists
__XX: Category:Women scientists
  • Combinations (4) of 1 element
X___: Category:Americans
_X__: Category:Jews
__X_: Category:Women
___X: Category:Scientists
  • Combination (1) of 0 element
____: Category:Contents
  • 1 + 4 + 6 + 4 + 1 = 16 = 2 × 2 × 2 × 2

Five elements in a category name

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  • Combination (1) of 5 elements
XXXXX: Category:Lists of American Jewish women scientists
  • Combinations (5) of 4 elements
XXXX_: Category:Lists of American Jewish women
XXX_X: Category:Lists of American Jewish scientists
XX_XX: Category:Lists of American women scientists
X_XXX: Category:Lists of Jewish women scientists
_XXXX: Category:American Jewish women scientists
  • Combinations (10) of 3 elements
XXX__: Category:Lists of American Jews
XX_X_: Category:Lists of American women
XX__X: Category:Lists of American scientists
X_XX_: Category:Lists of Jewish women
X_X_X: Category:Lists of Jewish scientists
X__XX: Category:Lists of women scientists
_XXX_: Category:American Jewish women
_XX_X: Category:American Jewish scientists
_X_XX: Category:American women scientists
__XXX: Category:Jewish women scientists
  • Combinations (10) of 2 elements
XX___: Category:Lists of Americans
X_X__: Category:Lists of Jews
X__X_: Category:Lists of women
X___X: Category:Lists of scientists
_XX__: Category:American Jews
_X_X_: Category:American women
_X__X: Category:American scientists
__XX_: Category:Jewish women
__X_X: Category:Jewish scientists
___XX: Category:Women scientists
  • Combinations (5) of 1 element
X____: Category:Lists
_X___: Category:Americans
__X__: Category:Jews
___X_: Category:Women
____X: Category:Scientists
  • Combination (1) of 0 element
_____: Category:Contents
  • 1 + 5 + 10 + 10 + 5 + 1 = 32 = 2 × 2 × 2 × 2 × 2

Six elements in a category name

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  • Combination (1) of 6 elements
XXXXXX: Category:Lists of award-winning American Jewish women scientists
  • Combinations (6) of 5 elements
XXXXX_: Category:Lists of award-winning American Jewish women
XXXX_X: Category:Lists of award-winning American Jewish scientists
XXX_XX: Category:Lists of award-winning American women scientists
XX_XXX: Category:Lists of award-winning Jewish women scientists
X_XXXX: Category:Lists of American Jewish women scientists
_XXXXX: Category:Award-winning American Jewish women scientists
  • Combinations (15) of 4 elements
XXXX__: Category:Lists of award-winning American Jews
XXX_X_: Category:Lists of award-winning American women
XXX__X: Category:Lists of award-winning American scientists
XX_XX_: Category:Lists of award-winning Jewish women
XX_X_X: Category:Lists of award-winning Jewish scientists
XX__XX: Category:Lists of award-winning women scientists
X_XXX_: Category:Lists of American Jewish women
X_XX_X: Category:Lists of American Jewish scientists
X_X_XX: Category:Lists of American women scientists
X__XXX: Category:Lists of Jewish women scientists
_XXXX_: Category:Award-winning American Jewish women
_XXX_X: Category:Award-winning American Jewish scientists
_XX_XX: Category:Award-winning Americanh women scientists
_X_XXX: Category:Award-winning Jewish women scientists
__XXXX: Category:American Jewish women scientists
  • Combinations (20) of 3 elements
XXX___: Category:Lists of award-winning Americans
XX_X__: Category:Lists of award-winning Jews
XX__X_: Category:Lists of award-winning women
XX___X: Category:Lists of award-winning scientists
X_XX__: Category:Lists of American Jews
X_X_X_: Category:Lists of American women
X_X__X: Category:Lists of American scientists
X__XX_: Category:Lists of Jewish women
X__X_X: Category:Lists of Jewish scientists
X___XX: Category:Lists of women scientists
_XXX__: Category:Award-winning American Jewish
_XX_X_: Category:Award-winning American women
_XX__X: Category:Award-winning American scientists
_X_XX_: Category:Award-winning Jewish women
_X_X_X: Category:Award-winning Jewish scientists
_X__XX: Category:Award-winning women scientists
__XXX_: Category:American Jewish women
__XX_X: Category:American Jewish scientists
__X_XX: Category:American women scientists
___XXX: Category:Jewish women scientists
  • Combinations (15) of 2 elements
XX____: Category:Lists of award-winners
X_X___: Category:Lists Americans
X__X__: Category:Lists of Jews
X___X_: Category:Lists of women
X____X: Category:Lists of scientists
_XX___: Category:Award-winning Americans
_X_X__: Category:Award-winning Jews
_X__X_: Category:Award-winning women
_X___X: Category:Award-winning scientists
__XX__: Category:American Jews
__X_X_: Category:American women
__X__X: Category:American scientists
___XX_: Category:Jewish women
___X_X: Category:Jewish scientists
____XX: Category:Women scientists
  • Combination (6) of 1 element
X_____: Category:Lists
_X____: Category:Award-winners
__X___: Category:Americans
___X__: Category:Jews
____X_: Category:Women
_____X: Category:Scientists
  • Combination (1) of 0 element
______: Category:Contents
  • 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64 = 2 × 2 × 2 × 2 × 2 × 2

See also

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