Irrational dilations of Pascal's triangle

D. Berend; M. D. Boshernitzan; G. Kolesnik

doi:10.1112/S0025579300014418

Irrational dilations of Pascal's triangle

D. Berend, M. D. Boshernitzan, G. Kolesnik

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

Let (b_n) be a sequence of integers, obtained by traversing the rows of Pascal's triangle, as follows: start from the element at the top of the triangle, and at each stage continue from the current element to one of the elements at the next row, either the one immediately to the left of the current element or the one immediately to its right. Consider the distribution of the sequence (b_nα) modulo 1 for an irrational a. The main results show that this sequence "often" fails to be uniformly distributed modulo 1, and provide answers to some questions raised by Adams and Petersen.

Original language	English
Pages (from-to)	159-168
Number of pages	10
Journal	Mathematika
Volume	48
Issue number	1-2
DOIs	https://doi.org/10.1112/S0025579300014418
State	Published - 1 Jan 2001

ASJC Scopus subject areas

Mathematics (all)

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abstract = "Let (bn) be a sequence of integers, obtained by traversing the rows of Pascal's triangle, as follows: start from the element at the top of the triangle, and at each stage continue from the current element to one of the elements at the next row, either the one immediately to the left of the current element or the one immediately to its right. Consider the distribution of the sequence (bnα) modulo 1 for an irrational a. The main results show that this sequence {"}often{"} fails to be uniformly distributed modulo 1, and provide answers to some questions raised by Adams and Petersen.",

author = "D. Berend and Boshernitzan, {M. D.} and G. Kolesnik",

note = "Funding Information: Acknowledgement. The authors wish to express their gratitude to Jean-Paul Allouche for drawing their attention to [1], and to Karl Petersen for his helpful comments on the first draft of the paper. The research of the first author was supported in part by the Basic Research Foundation, and that of the first two by the Bi-National Israel-USA Science Foundation.",

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N2 - Let (bn) be a sequence of integers, obtained by traversing the rows of Pascal's triangle, as follows: start from the element at the top of the triangle, and at each stage continue from the current element to one of the elements at the next row, either the one immediately to the left of the current element or the one immediately to its right. Consider the distribution of the sequence (bnα) modulo 1 for an irrational a. The main results show that this sequence "often" fails to be uniformly distributed modulo 1, and provide answers to some questions raised by Adams and Petersen.

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Irrational dilations of Pascal's triangle

Abstract

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