The simplest 2-regular sequences

Activity: Talk or presentation Oral presentation


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.
Period14 Dec 2023
Held atInstitute of Applied Physics, Austria
Degree of RecognitionNational


  • Regular sequences
  • Low discrepancy sequences
  • Sierpinski triangle