Discrepancy of LS-sequences of partitions

TL;DR

This paper provides precise estimates of the discrepancy for a class of uniformly distributed partition sequences, highlighting those with low discrepancy, including the Kakutani-Fibonacci sequence.

Contribution

It introduces a detailed discrepancy analysis for a broad class of partition sequences, identifying sequences with optimal low discrepancy properties.

Findings

Identified a large class of low-discrepancy partition sequences

Provided precise discrepancy estimates for these sequences

Included the Kakutani-Fibonacci sequence as a notable example

Abstract

In this paper we give a precise estimate of the discrepancy of a class of uniformly distributed sequences of partitions. Among them we found a large class having low discrepancy (which means of order 1/N. One of them is the Kakutani-Fibonacci sequence.