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 k {\textstyle k} elements are greater than the previous element (permutations with k {\textstyle k} "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis.
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 k {\textstyle k} elements are greater than the previous element (permutations with k {\textstyle k} "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis.
Source: Wikipedia "Eulerian number" · CC BY-SA 4.0
Share this article: X · Bluesky