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combinatorics

Combinatorial proof

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Algebraic versus combinatorial proof Bijective proof as a technique Choosing an identity-proving strategy Proving Pascal's identity combinatorially Proving a subset-sum identity combinatorially Proving the hockey-stick identity combinatorially Combinatorial proof of binomial identities Double counting as a technique Proving inclusion-exclusion by counting What a combinatorial proof requires Combinatorial proof Existence proofs Multinomial coefficients Overcounting and dividing out Pascal's identity as a proof tool Proof by cases Proof by contradiction Proof by contrapositive Proving set identities two ways The general inclusion-exclusion formula The hockey-stick identity Binomial coefficients and Pascal's triangle Direct proof Combinations Definitions are the raw material of a proof Divisibility, parity, and remainders

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