The Lucas congruence for 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 کاملCongruence Problems Involving Stirling Numbers of the First Kind
It is by now well known that the parities of the binomial coefficients show a fractal-like appearance when plotted in the x-y plane. Similarly, if f(n,k) is some counting sequence and/? is a prime, we can plot an asterisk at (//,&) iff(n,k) # 0 (mod/?), and a blank otherwise, to get other complex, and often interesting, patterns. For the ordinary and Gaussian binomial coefficients and for the S...
متن کاملCongruence Classes of 2-adic Valuations of Stirling Numbers of the Second Kind
We analyze congruence classes of S(n, k), the Stirling numbers of the second kind, modulo powers of 2. This analysis provides insight into a conjecture posed by Amdeberhan, Manna and Moll, which those authors established for k at most 5. We provide a framework that can be used to justify the conjecture by computational means, which we then complete for values of k between 5 and 20.
متن کاملGeneralized Convolution Identities for Stirling Numbers of the Second Kind
We prove an identity for sums of products of an arbitrary fixed number of Stirling numbers of the second kind; this can be seen as a generalized convolution identity. As a consequence we obtain two polynomial identities that also involve Stirling numbers of the second kind.
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: Acta Arithmetica
سال: 2000
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-94-1-41-52