Category
page 1Theorems in discrete mathematics
pigeonhole principle
mathematical lemma that, if 𝑛 items are put into 𝑚 containers, with 𝑛>𝑚, then at least one container must contain more than one item
Minimax
Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of u
Arrow's impossibility theorem
Result that no ranked-choice system is spoilerproof
Noisy-channel coding theorem
limit on data transfer rate
Myhill–Nerode theorem
theorem
Erdős–Szekeres theorem
theorem that sufficiently long sequences of numbers have long monotonic subsequences
Sprague–Grundy theorem
theorem in combinatorial game theory that every impartial game position is equivalent to a position in the game of nim
Gibbard–Satterthwaite theorem
theorem that deterministic ordinal electoral systems that choose a single winner are either dictatorial, binary choice, or susceptible to tactical voting
Van der Waerden's theorem
theorem on arithmetic progressions
Kruskal's tree theorem
well-quasi-ordering of finite trees
theorem on friends and strangers
theorem
Hales–Jewett theorem
on how much high-dimensional objects must exhibit some combinatorial structure
Akra–Bazzi method
on divide and conquer algorithms where the sub-problems have substantially different sizes
Holland's schema theorem
theorem on genetic algorithms
May's theorem
Social Choice theory on voting
Cameron–Erdős conjecture
Theorem on the number of sum-free sets contained in 1,...,N
Erdős–Ko–Rado theorem
theorem on the maximum size of a family of pairwise intersecting sets
Erdős–Anning theorem
infinite set of points in R2 with mutual integer distances must be a straight line
Erdős–Szemerédi theorem
Dinitz conjecture
theorem in combinatorics on the extension of arrays to partial Latin squares