Applied Combinatorics is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá …

What is combinatorics used for?

Combinatorics methods can be used to develop estimates about how many operations a computer algorithm will require. Combinatorics is also important for the study of discrete probability. Combinatorics methods can be used to count possible outcomes in a uniform probability experiment.

What is combinatorics the study of?

combinatorics, also called combinatorial mathematics, the field of mathematics concerned with problems of selection, arrangement, and operation within a finite or discrete system.