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 ...
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In this paper, we consider translation and multiplication operators acting on the rings of symmetric and nonsymmetric polynomials and study their matrix coefficients with respect to the bases of Jack polynomials and interpolation polynomials. The main new insight is that the symmetric and nonsymmetric cases share a key combinatorial feature, that of a locally finite graded poset with a minimum ...
متن کاملNew Congruences for Central Binomial Coefficients
Let p be a prime and let a be a positive integer. In this paper we determine ∑pa−1 k=0 ( 2k k+d ) /mk and ∑p−1 k=1 ( 2k k+d ) /(kmk−1) modulo p for all d = 0, . . . , pa, where m is any integer not divisible by p. For example, we show that if p 6= 2, 5 then p−1 ∑
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In this paper we establish some new congruences involving central binomial coefficients as well as Catalan numbers. Let p be a prime and let a be any positive integer. We determine ∑pa−1 k=0 ( 2k k+d ) mod p2 for d = 0, . . . , pa and ∑pa−1 k=0 ( 2k k+δ ) mod p3 for δ = 0, 1. We also show that
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1999
ISSN: 0022-247X
DOI: 10.1006/jmaa.1999.6420