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 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.

  3. Hardy–Ramanujan–Littlewood circle method - Wikipedia

    en.wikipedia.org/wiki/HardyRamanujan...

    The initial idea is usually attributed to the work of Hardy with Srinivasa Ramanujan a few years earlier, in 1916 and 1917, on the asymptotics of the partition function.It was taken up by many other researchers, including Harold Davenport and I. M. Vinogradov, who modified the formulation slightly (moving from complex analysis to exponential sums), without changing the broad lines.

  4. Integer partition - Wikipedia

    en.wikipedia.org/wiki/Integer_partition

    2 + 1 + 1 1 + 1 + 1 + 1. The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1. An individual summand in a partition is called a part.

  5. Hardy–Ramanujan theorem - Wikipedia

    en.wikipedia.org/wiki/HardyRamanujan_theorem

    In mathematics, the HardyRamanujan theorem, proved by Ramanujan and checked by Hardy [1] states that the normal order of the number () of distinct prime factors of a number is ⁡ ⁡. Roughly speaking, this means that most numbers have about this number of distinct prime factors.

  6. 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.

  7. Donald J. Newman - Wikipedia

    en.wikipedia.org/wiki/Donald_J._Newman

    He gave simple proofs of the prime number theorem and the HardyRamanujan partition formula. He excelled on multiple occasions at the annual Putnam competition while studying at City College of New York and New York University, and later received his PhD from Harvard University in 1953. [2]

  8. AOL Mail

    mail.aol.com

    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  9. Partition function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Partition_function...

    The partition function is commonly used as a probability-generating function for expectation values of various functions of the random variables. So, for example, taking β {\displaystyle \beta } as an adjustable parameter, then the derivative of log ⁡ ( Z ( β ) ) {\displaystyle \log(Z(\beta ))} with respect to β {\displaystyle \beta }