Area
Combinatorics
49 concepts in 11 topics and 2 courses. Explore freely or follow a guided course.
49concepts
11topics
2courses
Courses
Enumerative combinatorics
Generating functions 3 · Classical combinatorial numbers 7 · Compositions and partitions 4 · Symmetry and counting 2 · Posets and lattices 2 · Extremal combinatorics 1
Discrete mathematics
Proofs and induction 4 · Sets and relations 4 · Counting 8 · Graph theory 10 · Recurrences and arithmetic 7
Topics
Generating functions 3 concepts
Multinomial coefficient · Exponential generating function · Binomial coefficient
Classical combinatorial numbers 7 concepts
Stirling number of the second kind · Bell number · Stirling number of the first kind · Catalan number · Derangement · Cycle of a permutation · Inclusion-exclusion principle
Compositions and partitions 4 concepts
Integer composition · Integer partition · Partition generating function · Pentagonal number theorem
Symmetry and counting 2 concepts
Posets and lattices 2 concepts
Extremal combinatorics 1 concepts
Proofs and induction 4 concepts
Direct proof · Proof by contradiction · Mathematical induction · Strong induction
Sets and relations 4 concepts
Inclusion-exclusion principle · Partial order relation · Set operations · Hasse diagram
Counting 8 concepts
Binomial coefficient · Multiplication principle · Factorial · Permutations with repetition · Pigeonhole principle · Binomial theorem · Combinations with repetition · Permutations and combinations
Graph theory 10 concepts
Graph · Degree of a vertex · Path in a graph · Connected graph · Tree · Eulerian cycle · Hamiltonian cycle · Bipartite graph · Graph coloring · Planar graph
Recurrences and arithmetic 7 concepts
Recurrence relation · Divisibility · Greatest common divisor · Euclidean algorithm · Modular congruence · Homogeneous linear recurrence · Prime number