permutations
All possible orderings
Permutations are the different arrangements possible when ordering a set of things.
In mathematics, permutation refers specifically to arrangements where order matters—the permutations of ABC include ACB, BAC, BCA, CAB, and CBA.
More loosely, permutations are variations or different versions: The idea has gone through countless permutations since we first proposed it.
The singular permutation appears in both technical and general contexts.
Unions of separate parts
- factorialDescending multiplication of integers
- enumerationSequential listing of items
- arrangementOrdered configuration or agreement
- rearrangementAltered ordering of elements
counting · binomial · multinomial · selection · ordering · lexicographic · recursive · repetition
Assembled collection of things
- symmetryInvariance under transformation
- cycleRepeating sequence of events
- transpositionSwapping positions of elements
- identityWho someone is
inverse · composition · conjugate · orbit · stabilizer · generator · order · parity
Occurring without pattern
- shuffleRandomize by mixing
- lotteryRandomized prize distribution
- samplingExtracting subset for study
- distributionAllocation across recipients
outcome · chance · randomization · scramble · draw · arrangement · disorder · entropy
Modified versions of something
- possibilitiesThings that may occur
- optionsAvailable courses of action
- alternativesOther available options
- versionsDistinct forms or renditions
combinations · configurations · iterations · scenarios · outcomes · arrangements · diversity · multiplicity
Arrangement of parts
- orderingPlacing in sequence
- sequenceOrdered succession of elements
- layoutSpatial arrangement of elements
- patternRecurring arrangement or template
rearrangement · variation · combination · lineup · setup · organization · array · placement
combinations
Unions of separate parts
- factorialDescending multiplication of integers
- enumerationSequential listing of items
- arrangementOrdered configuration or agreement
rearrangement · counting · binomial · multinomial · selection · ordering · lexicographic · recursive · repetition · formula
group
Assembled collection of things
- symmetryInvariance under transformation
- cycleRepeating sequence of events
- transpositionSwapping positions of elements
identity · inverse · composition · conjugate · orbit · stabilizer · generator · order · parity · even
random
Occurring without pattern
distribution · outcome · chance · randomization · scramble · draw · arrangement · disorder · entropy · Monte Carlo
variations
Modified versions of something
- possibilitiesThings that may occur
- optionsAvailable courses of action
- alternativesOther available options
versions · combinations · configurations · iterations · scenarios · outcomes · arrangements · diversity · multiplicity · range
configuration
Arrangement of parts
- orderingPlacing in sequence
- sequenceOrdered succession of elements
- layoutSpatial arrangement of elements
pattern · rearrangement · variation · combination · lineup · setup · organization · array · placement · disposition
- mathaddition, subtraction, multiplication, division, algebra
- math conceptsangle, numbers, algebra, circle, equations
- probabilityprobability, chance, random, randomness, odds
- discrete mathcombinatorics, graph theory, set theory, number theory, proofs
- Kabbalahhod, Tree of Life, tree of life, divine spark, sparks
- algorithmsalgorithm, algorithms, DFS, binary search, A star
permutationscombinations
Unions of separate parts
subsets · groupings · selections · collections · sets
permutationsconstant
Fixed, unvarying quantity
invariant · singular form · permanence · uniformity · fixity