Classical combinatorial numbers

Concepts

• Inclusion-exclusion principle from Discrete mathematics 10 exercisesIt counts the elements of the union of finite sets A, B, C, … by adding their sizes and correcting what was counted too often in…
• Cycle of a permutation from Modern algebra I 10 exercisesA cycle of length k in S_n is a permutation sending a_1mapsto a_2mapstocdotsmapsto a_kmapsto a_1 and fixing all other elements.
• Stirling number of the second kind 10 exercisesThe Stirling number of the second kind S(n,k) counts the partitions of a set of n elements into k nonempty, indistinguishable blo…
• Bell number 10 exercisesThe Bell number B_n is the number of partitions of a set with n elements, that is, of ways to split it into nonempty disjoint sub…
• Stirling number of the first kind 10 exercisesThe Stirling number of the first kind c(n,k) counts the permutations of n elements that have exactly k cycles.
• Catalan number 10 exercisesThe Catalan number C_n counts, among many other structures, the triangulations of a convex polygon with n+2 sides and the Dyck pa…
• Derangement 10 exercisesA derangement is a permutation of n elements with no fixed points; the number of derangements is D_n.