Integer Binomial Plan: a Generalization on Factorials and Binomial Coefficients
نویسندگان
چکیده
منابع مشابه
The Sum of Binomial Coefficients and Integer Factorization
The combinatorial sum of binomial coe cients n i r (a) := X k⌘i (mod r) ✓ n k ◆ a k has been studied widely in combinatorial number theory, especially when a = 1 and a = 1. In this paper, we connect it with integer factorization for the first time. More precisely, given a composite n, we prove that for any a coprime to n there exists a modulus r such that the combinatorial sum has a nontrivia...
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We prove a simple relationship between extended binomial coefficients — natural extensions of the well-known binomial coefficients — and weighted restricted integer compositions. Moreover, we give a very useful interpretation of extended binomial coefficients as representing distributions of sums of independent discrete random variables. We apply our results, e.g., to determine the distribution...
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Binomial coefficients arise naturally in combinatorics. Recently the speaker initiated the study of certain divisibility properties of binomial coefficients, and products or sums of binomial coefficients. In this talk we introduce the speaker’s related results and various conjectures. The materials come from the author’s two preprints: 1. Z. W. Sun, Products and sums divisible by central binomi...
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In this paper we study recurrences concerning the combinatorial sum [n r ] m = ∑ k≡r (mod m) (n k ) and the alternate sum ∑ k≡r (mod m)(−1) (n k ) , where m > 0, n > 0 and r are integers. For example, we show that if n > m−1 then b(m−1)/2c ∑ i=0 (−1) (m− 1− i i )[n− 2i r − i ]
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ژورنال
عنوان ژورنال: Journal of Mathematics Research
سال: 2010
ISSN: 1916-9809,1916-9795
DOI: 10.5539/jmr.v2n3p18