Combinatorics

Special Numbers

Bell Number

• number of different partitions of n elements
• http://mathworld.wolfram.com/BellNumber.html
• strong resemblance to 2nd Kind Stirling Number: $B_n = \sum_{k = 0}^{n} S(n, k)$.
• Calculation: Bell's Triangle

Eulerian Number E(n, k)

• number of permutations of {1, 2, ..., n} which have k ascents
• E(n, k) = E(n, n - 1 - k)
• E(n, k) = (k + 1)E(n - 1, k) + (n - k)E(n - 1, k - 1)

Problems

• mathematician-language problem.

Last Modified: October 22, 2011 22:04:02