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Discrete Mathematics

Discrete Mathematics

The Wolfram Language 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.

List and Set Operations »

Tuples   Subsets   Union   Intersection   Complement   DisjointQ   ...

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 Networks »

Graph represent an undirected, directed, or mixed graph, or a multigraph

FindShortestPath   FindCycle   FindGraphIsomorphism   ...

Trees & Expression Enumeration

TreeGraph   KaryTree   FindSpanningTree   ClusteringTree   ...

Groupings generate all possible tree expressions from lists of elements

Combinatorial Optimization

FindMinimum , Minimize solve integer programming problems

FindShortestTour solve traveling salesman problems

KnapsackSolve   FrobeniusSolve

Boolean Computation »

And   Or   SatisfiableQ   BooleanFunction   BooleanMinimize   ...

Algebraic Systems »

FiniteGroupData   LatticeData   KnotData

Computational Systems »

CellularAutomaton   TuringMachine   SubstitutionSystem   RulePlot

Cryptography »

Encrypt   Decrypt   GenerateSymmetricKey   ...

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