The Fibonacci partition triangles
نویسندگان
چکیده
منابع مشابه
Fibonacci words in hyperbolic Pascal triangles
The hyperbolic Pascal triangle HPT 4,q (q ≥ 5) is a new mathematical construction, which is a geometrical generalization of Pascal’s arithmetical triangle. In the present study we show that a natural pattern of rows of HPT 4,5 is almost the same as the sequence consisting of every second term of the well-known Fibonacci words. Further, we give a generalization of the Fibonacci words using the h...
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It is known that if Ln, respectively Rn9 are n x n matrices with the (/, j ) * entry the binomial coefficient (y~l)? respectively (^l)), then Ln = In (mod 2), respectively R„=In (mod 2), where In is the identity matrix of dimension n>\ (see, e.g., Problem PI 073 5 in the May 1999 issue of Arner. Math Monthly). The entries of Ln form a left-justified Pascal triangle and the entries of Rn result ...
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where m is a positive integer, <jJ= (1 + 15)/2, n ranges over all the positive integers, and fp (x) denotes the fractional part of x. (We depart from the standard notation where (x) denotes the fractional part of x to avoid confusion in complicated expressions. See Lemma 4.4 below, for instance.) We shall also prove the following conjecture of Chris Long [4]: the set A satisfies the equality A ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2012
ISSN: 0001-8708
DOI: 10.1016/j.aim.2012.04.010