Institution: Stanford University, Department of Computer Science

Title: On the gap structure of sequences of points on a circle

Author: Ramshaw, Lyle H.

Date: November 1977

Abstract: Considerable mathematical effort has gone into studying sequences of points in the interval (0,1) which are evenly distributed, in the sense that certain intervals contain roughly the correct percentages of the first n points. This paper explores the related notion in which a sequence is evenly distributed if its first n points split a given circle into intervals which are roughly equal in length, regardless of their relative positions. The sequence $x_k$ = ($\log_2$(2k-1) mod 1) was introduced in this context by DeBruijn and Erdoes. We will see that the gap structure of this sequence is uniquely optimal in a certain sense, and optimal under a wide class of measures.

http://i.stanford.edu/pub/cstr/reports/cs/tr/77/637/CS-TR-77-637.pdf