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  2. 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 ...

  3. 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]

  4. 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 ...

  5. Quotition and partition - Wikipedia

    en.wikipedia.org/wiki/Quotition_and_partition

    The answer to the question "How many cartons are needed to fit 45 eggs?" is 4 cartons, since = + rounds up to 4. Quotition is the concept of division most used in measurement. For example, measuring the length of a table using a measuring tape involves comparing the table to the markings on the tape.

  6. Glaisher's theorem - Wikipedia

    en.wikipedia.org/wiki/Glaisher's_theorem

    In number theory, Glaisher's theorem is an identity useful to the study of integer partitions.Proved in 1883 [1] by James Whitbread Lee Glaisher, it states that the number of partitions of an integer into parts not divisible by is equal to the number of partitions in which no part is repeated or more times.

  7. Orders of magnitude (data) - Wikipedia

    en.wikipedia.org/wiki/Orders_of_magnitude_(data)

    0.415 bits (log 2 4/3) – amount of information needed to eliminate one option out of four. 0.6–1.3 bits – approximate information per letter of English text. [3] 2 0: bit: 10 0: bit 1 bit – 0 or 1, false or true, Low or High (a.k.a. unibit) 1.442695 bits (log 2 e) – approximate size of a nat (a unit of information based on natural ...

  8. Rogers–Ramanujan identities - Wikipedia

    en.wikipedia.org/wiki/Rogers–Ramanujan_identities

    The number of partitions of such that the adjacent parts differ by at least 2 is the same as the number of partitions of such that each part is congruent to either 1 or 4 modulo 5. The number of partitions of such that the adjacent parts differ by at least 2 and such that the smallest part is at least 2 is the same as the number of partitions ...

  9. 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. [18] It is denoted by S r ( n , k ) {\displaystyle S_{r}(n,k)} and obeys the recurrence relation