Irrational dilations of Pascal's triangle Academic Article uri icon

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 n α) 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.

publication date

  • January 1, 2001