Note on some restricted Stirling numbers of the second kind
نویسندگان
چکیده
منابع مشابه
Stirling Numbers of the Second Kind
The papers [18], [9], [21], [14], [23], [6], [24], [2], [3], [8], [10], [1], [22], [7], [11], [20], [16], [19], [4], [5], [13], [12], [17], and [15] provide the terminology and notation for this paper. For simplicity, we adopt the following convention: k, l, m, n, i, j denote natural numbers, K, N denote non empty subsets of N, K1, N1, M1 denote subsets of N, and X, Y denote sets. Let us consid...
متن کاملMaximum Stirling Numbers of the Second Kind
Say an integer n is exceptional if the maximum Stirling number of the second kind S(n, k) occurs for two (of necessity consecutive) values of k. We prove that the number of exceptional integers less than or equal to x is O(x), for any ! > 0. We derive a similar result for partitions of n into exactly k integers.
متن کاملON (q; r; w)-STIRLING NUMBERS OF THE SECOND KIND
In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly de ned (q; r; w)Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q...
متن کاملOn some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind
Let S(n, k) be the classical Stirling numbers of the second kind, d > 1 be an integer, and P,Q,R ∈ Q[X1, . . . , Xm] be nonconstant polynomials such that P does not divide Q and R is not a dth power. We prove that if k1, . . . , km are any sufficiently large distinct positive integers then, setting Si = S(n, ki), Q(S1,...,Sm) P (S1,...,Sm) ∈ Z for only finitely many n ∈ N and R(S1, . . . , Sm) ...
متن کاملA Summation Rule Using Stirling Numbers of the Second Kind
n m n m Z ^ . W" = 5>(w, jy^Fip, k)(k)j = Zj\S(m, j)(n, j). k=o y=o k=o j=o Notice that the special case for m = 0 is also true. Hence, (2) holds for every m > 0. • Remark Sometimes in applications of the rule function F(n, k) may involve some independent parameters. Moreover, for the particular case in which F(n, k) > 0, so that (j)(n, 0) > 0, the lefthand side of (2) divided by (j)(n, 0) m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2016
ISSN: 1631-073X
DOI: 10.1016/j.crma.2015.12.003