Combinatorics
Explore basic counting; counting structures; partitions and symmetry. Concepts and connections are available independently of video coverage.
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Pigeonhole principle
More objects than boxes force at least one box to contain multiple objects.
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Combinations
Choose k distinct elements from an n-element set without order, for integers . Each chosen subset corresponds to k!()! full permutations. Repetition-allowed selections are a different counting problem and need their own assumptions.
Combinatorial counting
Count finite outcomes with disjoint-case sums, successive-choice products and equal-fiber division or bijections. Check that cases are disjoint and multiplicities are constant. Multiplication of choice counts is not a probability-independence assumption.
Generating functions
A sequence encoded as series coefficients supports algebraic counting and recurrence calculations.
Inclusion–exclusion
Alternating intersection counts correct double-counting in unions of finite sets.
Algorithmic complexity
Time and space requirements are expressed as functions of input size under a computational model.
Knowledge connections
- Inclusion–exclusion · Related · Map context
- Generating functions · Related · Map context
- Combinations · Related · Map context
- Combinatorial counting · Related · Map context
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Discrete Mathematics: Counting and Number Theory
Connect functions and counting with elementary number theory, graph structures and algorithmic reasoning. Shared concepts and reviewed map connections organize the path; video explanations are added as resources pass review.