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Irrational dilations of Pascal's triangle
Author(s) -
Berend D.,
Boshernitzan M. D.,
Kolsenik G.
Publication year - 2001
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014418
Subject(s) - mathematics , irrational number , modulo , combinatorics , element (criminal law) , sequence (biology) , pascal (unit) , row , discrete mathematics , geometry , law , computer science , database , genetics , programming language , biology , political science
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 n α ) modulo 1 for an irrational α . 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.