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  2. Integer partition - Wikipedia

    en.wikipedia.org/wiki/Integer_partition

    In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.)

  3. Partition function (number theory) - Wikipedia

    en.wikipedia.org/wiki/Partition_function_(number...

    The values (), …, of the partition function (1, 2, 3, 5, 7, 11, 15, and 22) can be determined by counting the Young diagrams for the partitions of the numbers from 1 to 8. In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n.

  4. Partition problem - Wikipedia

    en.wikipedia.org/wiki/Partition_problem

    Equal-cardinality partition is a variant in which both parts should have an equal number of items, in addition to having an equal sum. This variant is NP-hard too. [5]: SP12 Proof. Given a standard Partition instance with some n numbers, construct an Equal-Cardinality-Partition instance by adding n zeros. Clearly, the new instance has an equal ...

  5. Triangle of partition numbers - Wikipedia

    en.wikipedia.org/wiki/Triangle_of_partition_numbers

    In the number theory of integer partitions, the numbers () denote both the number of partitions of into exactly parts (that is, sums of positive integers that add to ), and the number of partitions of into parts of maximum size exactly .

  6. Composition (combinatorics) - Wikipedia

    en.wikipedia.org/wiki/Composition_(combinatorics)

    In mathematics, a composition of an integer n is a way of writing n as the sum of a sequence of (strictly) positive integers. Two sequences that differ in the order of their terms define different compositions of their sum, while they are considered to define the same integer partition of that number. Every integer has finitely many distinct ...

  7. Largest differencing method - Wikipedia

    en.wikipedia.org/wiki/Largest_differencing_method

    This solution is not optimal; a better partitioning is provided by the grouping ({5,5},{3,3,4},{1,4,5}). There is evidence for the good performance of LDM: [ 2 ] Simulation experiments show that, when the numbers are uniformly random in [0,1], LDM always performs better (i.e., produces a partition with a smaller largest sum) than greedy number ...

  8. Category:Integer partitions - Wikipedia

    en.wikipedia.org/wiki/Category:Integer_partitions

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  9. List of partition topics - Wikipedia

    en.wikipedia.org/wiki/List_of_partition_topics

    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