Group Seminar: Multivariate Algorithms and Quasi-Monte Carlo Methods

Lukas Spiegelhofer/TU Wien. Title: The simplest 2-regular sequences

Date: Thursday, November 14, 2023
Time: 10:15 am, S2 416-2

Abstract:

For an integer k greater than 1, k-regular sequences were defined by Allouche and Shallit.

We study two of the "simplest" such sequences, which are well-known:

(1.) the discrepancy of the van der Corput sequence, and (2.) the number of odd entries in a given row of Pascal's triangle.

In the first case, a Gaussian behaviour is known by previous results of Drmota, Larcher, and Pillichshammer; the second case gives rise to a constant (the Stolarsky--Harborth constant) whose precise value is still unknown.

We give an overview of these topics, and point out possible paths towards progress on these topics.