منابع مشابه
Geometry of Binomial Coefficients
This note describes the geometrical pattern of zeroes and ones obtained by reducing modulo two each element of Pascal's triangle formed from binomial coefficients. When an infinite number of rows of Pascal's triangle are included, the limiting pattern is found to be "self-similar," and is characterized by a "fractal dimension" log2 3. Analysis of the pattern provides a simple derivation of the ...
متن کاملPlanar Binomial Coefficients
The notion of binomial coefficients (T S ) of finite planar, reduced rooted trees T, S is defined and a recursive formula for its computation is shown. The nonassociative binomial formula (1 + x) = ∑
متن کاملOn the Conditioned Binomial Coefficients
We answer a question on the conditioned binomial coefficients raised in and article of Barlotti and Pannone, thus giving an alternative proof of an extension of Frobenius’ generalization of Sylow’s theorem.
متن کاملOn Divisibility concerning Binomial Coefficients
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...
متن کاملOn Sums of Binomial Coefficients
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: Discrete Applied Mathematics
سال: 2017
ISSN: 0166-218X
DOI: 10.1016/j.dam.2017.04.035