In combinatorics, the Eulerian number A ( n , k ) {\textstyle A(n,k)} is the number of permutations of the numbers 1 to n {\textstyle n} in which exactly...

In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...

node 2034 = number of unlabeled graphs on 11 nodes whose components are unicyclic graphs 2035 – Wolstenholme number 2036 – Eulerian number 2039 – Sophie...

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that...

the union of k ascending runs. The number of permutations of n with k ascents is (by definition) the Eulerian number ⟨ n k ⟩ {\displaystyle \textstyle...

month, the number of pairs of rabbits is equal to the number of mature pairs (that is, the number of pairs in month n – 2) plus the number of pairs alive...

26 sporadic simple groups. Sloane, N. J. A. (ed.). "Sequence A000295 (Eulerian numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation...

have even degree. All Eulerian circuits are also Eulerian paths, but not all Eulerian paths are Eulerian circuits. Euler's work was presented to the St...

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has...

hundred [and] eighty-four) is the natural number following 183 and preceding 185. There are 184 different Eulerian graphs on eight unlabeled vertices, and...

1/cosh t Eulerian numbers count certain types of permutations. Euler number (physics), the cavitation number in fluid dynamics. Euler number (algebraic...

the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...

Delannoy number Eulerian number Hypergeometric function List of factorial and binomial topics Macaulay representation of an integer Motzkin number Multiplicities...

the Euler diagram shows only relevant relationships. The first use of "Eulerian circles" is commonly attributed to Swiss mathematician Leonhard Euler (1707–1783)...

OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A008517 (Second-order Eulerian triangle T(n, k), 1 <= k <= n)". The On-Line Encyclopedia of Integer Sequences...

In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number...

}}={\frac {120}{5040}}={\frac {1}{42}}} There are formulas connecting Eulerian numbers ⟨n m⟩ to Bernoulli numbers: ∑ m = 0 n ( − 1 ) m ⟨ n m ⟩ = 2 n +...

group Bell numbers Boustrophedon transform Eulerian number Floyd's triangle Lozanić's triangle Narayana number Pascal's triangle Rencontres numbers Romberg's...

\rangle }\!\!{\bigg \rangle }} is a second-order Eulerian number. ω ( 0 ) = W 0 ( 1 ) ≈ 0.56714 ω ( 1 ) = 1 ω ( − 1 ± i π ) = − 1 ω...

mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer...

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with...

In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance...

highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive...

discrete mathematics, the BEST theorem gives a product formula for the number of Eulerian circuits in directed (oriented) graphs. The name is an acronym of...

long-standing problems that resist classical analytic approaches. See also: | Eulerian number | Multiple zeta values | Operad | Partially ordered set | Srinivasa...

In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p is prime...

triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...

integral graph—a graph whose spectrum consists entirely of integers. An Eulerian subgraph of a graph G {\displaystyle G} is a subgraph consisting of a subset...

In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is...

In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that...