combinatorics
Mathematics of arrangements
Combinatorics is the branch of mathematics concerned with counting, arranging, and selecting objects according to specified rules.
It deals with questions like how many ways items can be ordered, how many subsets exist within a set, or how many paths connect two points.
The field underlies probability theory, computer science, and optimization: Combinatorics tells us there are over 43 quintillion possible configurations of a Rubik's cube.
Arrangement in specific order
- enumerationSequential listing of items
- factorialDescending multiplication of integers
- multinomialExpression with several terms
- partitionBarrier separating spaces
Ordered succession of elements
- orderingPlacing in sequence
- arrangementOrdered configuration or agreement
- configurationArrangement of parts
- selectionChosen item or items
subset · tuple · lexicographic · anagram · placement · distribution
Finite problem-solving procedure
- constraintLimiting condition or rule
- feasibilityPotential for success
- complexityState of being complicated
- approximationNear but inexact value
Visual data display
- vertexPoint where edges converge
- edgeBoundary or sharpness
- pathRoute for traveling
- cycleRepeating sequence of events
tree · matching · coloring · planar · bipartite · adjacency · degree · subgraph
Randomly determined, statistically describable
- samplingExtracting subset for study
- distributionAllocation across recipients
- varianceSpread around the mean
permutation
Arrangement in specific order
- enumerationSequential listing of items
- factorialDescending multiplication of integers
- multinomialExpression with several terms
sequence
Ordered succession of elements
- orderingPlacing in sequence
- arrangementOrdered configuration or agreement
- configurationArrangement of parts
selection · subset · tuple · lexicographic · anagram · placement · distribution
algorithm
Finite problem-solving procedure
- constraintLimiting condition or rule
- feasibilityPotential for success
- complexityState of being complicated
graph
Visual data display
cycle · tree · matching · coloring · planar · bipartite · adjacency · degree · subgraph · clique
stochastic
Randomly determined, statistically describable
- samplingExtracting subset for study
- distributionAllocation across recipients
- varianceSpread around the mean
- mathaddition, subtraction, multiplication, division, algebra
- mathematicsalgebra, arithmetic, calculus, geometry, number
- probabilityprobability, chance, random, randomness, odds
- exact sciencesmathematics, physics, chemistry, math, algebra
- quantitative sciencesstatistics, mathematics, probability, calculus, algebra
- discrete mathgraph theory, set theory, number theory, proofs, sets
combinatoricsanalysis
Methodical study of parts
calculus · differential equations · topology · integral calculus · differential calculus