 partition

/pahr tish"euhn, peuhr/, n.1. a division into or distribution in portions or shares.2. a separation, as of two or more things.3. something that separates or divides.4. a part, division, or section.5. an interior wall or barrier dividing a room, area of a building, enclosure, etc., into separate areas.6. a septum or dissepiment, as in a plant or animal structure.7. Law. a division of property among joint owners or tenants in common or a sale of such property followed by a division of the proceeds.8. Logic. the separation of a whole into its integrant parts.9. Math.a. a mode of separating a positive whole number into a sum of positive whole numbers.b. the decomposition of a set into disjoint subsets whose union is the original set: A partition of the set (1, 2, 3, 4, 5) is the collection of subsets (1), (2, 3), (4), and (5).10. Rhet. (in a speech organized on classical principles) the second, usually brief section or part in which a speaker announces the chief lines of thought to be discussed in support of his or her theme.v.t.11. to divide into parts or portions.12. to divide or separate by interior walls, barriers, or the like (sometimes fol. by off): to partition off a dormitory into cubicles.13. to divide (a country or territory) into separate, usually differing political entities. Cf. Balkanize.14. Law. to divide property among several owners, either in specie or by sale and division of the proceeds.[140050; late ME < L partition (s. of partitio) division, equiv. to partit(us) ptp. of partiri to divide (see PARTY) + ion ION]Ant. 2. unity. 11. unite.
* * *
▪ of a setin mathematics and logic, division of a set of objects into a family of subsets that are mutually exclusive and jointly exhaustive; that is, no element of the original set is present in more than one of the subsets, and all the subsets together contain all the members of the original set.A related concept, central to the mathematical topics of combinatorics and number theory, is the partition of a positive integer—that is, the number of ways that an integer n can be expressed as the sum of k smaller integers. For example, the number of ways of representing the number 7 as the sum of 3 smaller whole numbers (n = 7, k = 3) is 4 (5 + 1 + 1, 4 + 2 + 1, 3 + 3 + 1, and 3 + 2 + 2).* * *
Universalium. 2010.