# Category:Combinatorics

This category contains results about Combinatorics.

Definitions specific to this category can be found in Definitions/Combinatorics.

**Combinatorics** is that branch of mathematics concerned with counting things.

**Combinatorial** problems are so named because they are exercises in counting the number of combinations of various objects.

## Subcategories

This category has the following 33 subcategories, out of 33 total.

### B

### C

### D

### L

### M

### N

### P

### R

### S

## Pages in category "Combinatorics"

The following 63 pages are in this category, out of 63 total.

### C

- Cardinality of Cartesian Product
- Cardinality of Complement
- Cardinality of Power Set of Finite Set
- Cardinality of Set of All Mappings
- Cardinality of Set of All Mappings from Empty Set
- Cardinality of Set of All Mappings to Empty Set
- Cardinality of Set of Bijections
- Cardinality of Set of Injections
- Cardinality of Set of Injections/Corollary
- Cardinality of Set of Strictly Increasing Mappings
- Cardinality of Set of Subsets
- Cardinality of Set of Surjections
- Cardinality of Set Union
- Cardinality of Set Union/Corollary
- Cardinality of Set Union/General Case
- Cayley's Formula
- Closed Form for Number of Derangements on Finite Set
- Count of Binary Operations on Set
- Count of Binary Operations with Fixed Identity
- Count of Binary Operations with Identity
- Count of Binary Operations Without Identity
- Count of Commutative Binary Operations on Set
- Count of Commutative Binary Operations with Fixed Identity
- Count of Commutative Binary Operations with Identity
- Count of Subsets with Even Cardinality
- Count of Subsets with Odd Cardinality
- Count of Truth Functions

### I

### N

- Necessary Conditions for Existence of Skolem Sequence
- Number of Compositions
- Number of Derangements
- Number of Derangements on Finite Set
- Number of Different n-gons that can be Inscribed in Circle
- Number of Different Ways to Colour the Faces of Cube with 3 Colours
- Number of Different Ways to Colour the Faces of Cube with 4 Colours
- Number of Different Ways to Colour the Faces of Cube with 5 Colours
- Number of Elements in Partition
- Number of Hamilton Cycles in Complete Graph
- Number of m-Cycles in Symmetric Group
- Number of Permutations
- Number of Set Partitions by Number of Components