The

Stirling number [s.sub.m,n] of the second kind is the number of ways to partition an m elements set into n nonempty subsets for any m, n [greater than or equal to] 0.

Let S(n, k) be the

Stirling number of the second kind, which counts the number of partitions of a set with n elements in k disjoint nonempty subsets.

For 1 [less than or equal to] k [less than or equal to] n, recall that the

Stirling number (of the second kind) Stir(n, k) counts the number of partitions of [n] with exactly k blocks.

Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the

Stirling number of the first kind (unsigned version).

Stirling number eight Gareth Flockhart then took advantage of a scrum 10 metres out to make the break for Barr to score.

Let [S.sub.n,m] denote the set of permutations of [S.sub.n] with m cycles, [s.sub.n,m], the unsigned

Stirling number of the first kind, denote the cardinality of [S.sub.n,m], and [mu] = m/n.

In particular, we determine the

stirling number of the second kind [s.sub.2](n, 4), when n [greater than or equal to] 4 is given.

(see [15, 16, 18-23]), where [S.sub.1](n, k) is the

Stirling numbers of the first kind and [S.sub.2](n, k) is the

Stirling numbers of the second kind as follows:

Combinatorial Identities for

Stirling Numbers: The Unpublished Notes of H.W.

The numbers [W.sub.m](n,k) can be shown to be a kind of generalization of the famous

Stirling numbers of the Second kind S(n, k) when the parameter m equals to 1.

This computation is based on some interesting relation between the dimensions of the summands of the [E.sub.2]-page of the spectral sequence and some

Stirling numbers. Since these Euler characteristic have an exponential growth, we deduce an exponential growth of the dimension of the associated graded space of [E.sub.2].

After preliminaries they cover numerical methods for solving ordinary and partial fractional differential equations, efficient numerical methods, generalized

Stirling numbers and applications, fractional variational principles, continuous-time random walks (CTRW) and fractional diffusion models, and applications of CTRW to finance and economics.