Discrete Mathematics

Mathematica has been used to make many important discoveries in discrete mathematics over the past two decades. Its integration of highly efficient and often original algorithms together with its high-level symbolic language has made it a unique environment for the exploration, development, and application of discrete mathematics.

ReferenceReference

List and Set Operations

Tuples ▪ Subsets ▪ Union ▪ Intersection ▪ Complement

Permutations »

Permutations ▪ Sort ▪ Ordering ▪ Signature ▪ RandomSample ▪ ...

Group Theory »

PermutationGroup ▪ GroupOrder ▪ GroupElements ▪ GroupElementQ ▪ ...

Enumeration-Related Functions »

Factorial ▪ Binomial ▪ Fibonacci ▪ StirlingS1 ▪ PartitionsP ▪ IntegerPartitions ▪ FiniteGroupCount ▪ ...

Discrete Calculus »

RSolve solve recurrence equations

Sum ▪ GeneratingFunction ▪ ZTransform ▪ DifferenceDelta ▪ ContinuedFractionK ▪ ...

Integer Sequences »

FindSequenceFunction find functions for integer sequences

RecurrenceTable ▪ LinearRecurrence ▪ ...

Strings and Digits

StringReplaceList ▪ IntegerDigits ▪ BitXor ▪ BitAnd

ReplaceList generate a list of forms matching a pattern

Graphs and Trees

GraphPlot, GraphPlot3D, LayeredGraphPlot lay out and draw graphs

TreePlot display trees

GraphData database of named and enumerated graphs and their properties

Combinatorial Optimization

FindMinimum, Minimize solve integer programming problems

FindShortestTour solve traveling salesman problems

Boolean Computation »

And ▪ Or ▪ SatisfiableQ ▪ BooleanFunction ▪ BooleanMinimize ▪ ...

Algebraic Systems »

FiniteGroupData ▪ LatticeData ▪ KnotData

Computational Systems »

CellularAutomaton ▪ TuringMachine

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