enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Partition function (number theory) - Wikipedia

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

    The function q(n) gives the number of these strict partitions of the given sum n. For example, q(3) = 2 because the partitions 3 and 1 + 2 are strict, while the third partition 1 + 1 + 1 of 3 has repeated parts. The number q(n) is also equal to the number of partitions of n in which only odd summands are permitted. [20]

  3. Integer partition - Wikipedia

    en.wikipedia.org/wiki/Integer_partition

    In the case of the number 4, partitions 4 and 1 + 1 + 1 + 1 are conjugate pairs, and partitions 3 + 1 and 2 + 1 + 1 are conjugate of each other. Of particular interest are partitions, such as 2 + 2, which have themselves as conjugate. Such partitions are said to be self-conjugate. [7] Claim: The number of self-conjugate partitions is the same ...

  4. Multiplicative partition - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_partition

    Because it is the fourth power of a prime, 81 has the same number (five) of multiplicative partitions as 4 does of additive partitions. The number 30 has five multiplicative partitions: 2 × 3 × 5 = 2 × 15 = 6 × 5 = 3 × 10 = 30.

  5. Stirling numbers of the second kind - Wikipedia

    en.wikipedia.org/wiki/Stirling_numbers_of_the...

    An r-associated Stirling number of the second kind is the number of ways to partition a set of n objects into k subsets, with each subset containing at least r elements. [17] It is denoted by S r ( n , k ) {\displaystyle S_{r}(n,k)} and obeys the recurrence relation

  6. Partition of a set - Wikipedia

    en.wikipedia.org/wiki/Partition_of_a_set

    Partitions of a 4-element set ordered by refinement. A partition α of a set X is a refinement of a partition ρ of X—and we say that α is finer than ρ and that ρ is coarser than α—if every element of α is a subset of some element of ρ. Informally, this means that α is a further fragmentation of ρ. In that case, it is written that ...

  7. Ramanujan's congruences - Wikipedia

    en.wikipedia.org/wiki/Ramanujan's_congruences

    In plain words, e.g., the first congruence means that If a number is 4 more than a multiple of 5, i.e. it is in the sequence 4, 9, 14, 19, 24, 29, . . . then the number of its partitions is a multiple of 5. Later other congruences of this type were discovered, for numbers and for Tau-functions.

  8. 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

  9. Triangle of partition numbers - Wikipedia

    en.wikipedia.org/wiki/Triangle_of_partition_numbers

    These two types of partition are in bijection with each other, by a diagonal reflection of their Young diagrams. Their numbers can be arranged into a triangle, the triangle of partition numbers , in which the n {\displaystyle n} th row gives the partition numbers p 1 ( n ) , p 2 ( n ) , … , p n ( n ) {\displaystyle p_{1}(n),p_{2}(n),\dots ,p ...