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  2. Eulerian number - Wikipedia

    en.wikipedia.org/wiki/Eulerian_number

    In combinatorics, the Eulerian number (,) is the number of permutations of the numbers 1 to in which exactly elements are greater than the previous element (permutations with "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis .

  3. Euler numbers - Wikipedia

    en.wikipedia.org/wiki/Euler_numbers

    The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic secant functions. The latter is the function in the definition. The latter is the function in the definition. They also occur in combinatorics , specifically when counting the number of alternating permutations of a set with an even number of elements.

  4. Eulerian path - Wikipedia

    en.wikipedia.org/wiki/Eulerian_path

    An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once. If such a cycle exists, the graph is called Eulerian or unicursal. [4] The term "Eulerian graph" is also sometimes used in a weaker sense to denote a graph where every vertex has even degree.

  5. Lucky numbers of Euler - Wikipedia

    en.wikipedia.org/wiki/Lucky_numbers_of_Euler

    Leonhard Euler published the polynomial k 2 − k + 41 which produces prime numbers for all integer values of k from 1 to 40. Only 6 lucky numbers of Euler exist, namely 2, 3, 5, 11, 17 and 41 (sequence A014556 in the OEIS). [1] Note that these numbers are all prime numbers. The primes of the form k 2 − k + 41 are

  6. List of topics named after Leonhard Euler - Wikipedia

    en.wikipedia.org/wiki/List_of_topics_named_after...

    Euler's number, e = 2.71828 . . . , the base of the natural logarithm; Euler's idoneal numbers, a set of 65 or possibly 66 or 67 integers with special properties; Euler numbers, integers occurring in the coefficients of the Taylor series of 1/cosh t; Eulerian numbers count certain types of permutations.

  7. Euler function - Wikipedia

    en.wikipedia.org/wiki/Euler_function

    The coefficient in the formal power series expansion for / gives the number of partitions of k.That is, = = ()where is the partition function.. The Euler identity, also known as the Pentagonal number theorem, is

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  9. Eisenstein integer - Wikipedia

    en.wikipedia.org/wiki/Eisenstein_integer

    an ordinary prime number (or rational prime) which is congruent to 2 mod 3 is also an Eisenstein prime. 3 and each rational prime congruent to 1 mod 3 are equal to the norm x 2 − xy + y 2 of an Eisenstein integer x + ωy .