Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are

• partition of a set or an ordered partition of a set,
• partition of a graph,
• partition of an integer,
• partition of an interval,
• partition of unity,
• partition of a matrix; see block matrix, and
• partition of the sum of squares in statistics problems, especially in the analysis of variance,
• quotition and partition, two ways of viewing the operation of division of integers.

Integer partitions

• Composition (combinatorics)
• Ewens's sampling formula
• Ferrers graph
• Glaisher's theorem
• Landau's function
• Partition function (number theory)
• Pentagonal number theorem
• Plane partition
• Quotition and partition
• Rank of a partition
  • Crank of a partition
• Solid partition
• Young tableau
• Young's lattice

Set partitions

• Bell number
• Bell polynomials
  • Dobinski's formula
• Cumulant
• Data clustering
• Equivalence relation
• Exact cover
  • Knuth's Algorithm X
    • Dancing Links
• Exponential formula
• Faà di Bruno's formula
• Feshbach–Fano partitioning
• Foliation
• Frequency partition
• Graph partition
• Kernel of a function
• Lamination (topology)
• Matroid partitioning
• Multipartition
• Multiplicative partition
• Noncrossing partition
• Ordered partition of a set
• Partition calculus
• Partition function (quantum field theory)
• Partition function (statistical mechanics)
  • Derivation of the partition function
• Partition of an interval
• Partition of a set
  • Ordered partition
  • Partition refinement
  • Disjoint-set data structure
• Partition problem
  • 3-partition problem
• Partition topology
• Quotition and partition
• Recursive partitioning
• Stirling number
  • Stirling transform
• Stratification (mathematics)
• Tverberg partition
• Twelvefold way