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combinatorics

The product rule

taught

Taught in

Requires

Nothing — this is foundational.

Required by

Local knowledge map

Local knowledge map

Choosing a counting method Choosing a group action to solve a counting problem Compositions of an integer Counting by cases Counting distinct colorings Counting distributions into boxes Counting injective functions Counting multinomial expansion terms Counting proper colorings Counting simple graphs by degree Counting surjective functions Counting the spanning trees of a small graph Counting trees versus counting graphs Counting with the complement Generating functions for counting problems Permutations Stars and bars with bounds Symmetry and combinatorial counting The pigeonhole principle Burnside's lemma Chromatic polynomials Counting labeled graphs Counting with trees Factorials Functions between finite sets, counted Stars and bars The sum rule The product rule Onto functions Orbits and stabilizers Rooted trees The chromatic number What a graph is

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.