Category
page 1Theorems in combinatorics
Hall's marriage theorem
theorem that a finite bipartite graph has a perfect matching iff any subset of vertices from one group has a neighbourhood of equal or greater size
Szemerédi's theorem
theorem that long dense subsets of the integers contain arbitrarily large arithmetic progressions
Dilworth's theorem
theorem that the maximum size of an antichain in a finite partial order equals the minimum number of chains into which it can be partitioned
Pólya enumeration theorem
theorem
Lagrange inversion theorem
theorem
Bertrand's ballot theorem
theorem that, in an election where candidate A receives 𝑝 votes and candidate B receives 𝑞 votes (𝑝>𝑞), the probability that A will be strictly ahead of B throughout the count is (𝑝−𝑞)/(𝑝+𝑞)
Szemerédi–Trotter theorem
bound on the number of incidences between points and lines in the plane
hockey-stick identity
recurrence relations of binomial coefficients in Pascal's triangle
Bruck–Ryser–Chowla theorem
a result on the combinatorics of block designs
Erdős–Rado theorem
theorem in combinatorial set theory
Baranyai's theorem
theorem