# Category:Combinatorics

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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.

It has been stated that it is the core of the discipline of discrete mathematics.

## Subcategories

This category has the following 52 subcategories, out of 52 total.

### B

- Birthday Paradox (3 P)

### C

- Cardinality of Power Set (5 P)
- Combinations with Repetition (1 P)
- Combinatorial Optimization (empty)
- Combinatorial Set Theory (empty)

### D

- Dirichlet's Box Principle (5 P)

### F

### H

- Hall's Marriage Theorem (4 P)

### I

### L

- Latin Squares (5 P)

### M

- Multinomial Coefficients (2 P)

### N

- Number of Permutations (11 P)

### P

- Product Rule for Counting (8 P)

### R

### S

## Pages in category "Combinatorics"

The following 68 pages are in this category, out of 68 total.

### C

- Cardinality of Cartesian Product of Finite Sets
- 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 Endorelations
- Cardinality of Set of Injections
- Cardinality of Set of Injections/Corollary
- Cardinality of Set of Relations
- Cardinality of Set of Strictly Increasing Mappings
- Cardinality of Set of Subsets
- Cardinality of Set of Surjections
- Cardinality of Set Union
- 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 Arrangements of n Objects of m Types
- Number of Compositions
- 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 k-Cycles in Symmetric Group
- Number of Permutations
- Number of Permutations with Repetition
- Number of Set Partitions by Number of Components
- Number of Ways of Seating People at Circular Table
- Number of Ways of Threading Beads on a Loop of Wire