Takagi Function Identities on Dyadic Rationals
Combinatorics
2024-08-06 v3 Data Structures and Algorithms
Classical Analysis and ODEs
Number Theory
Abstract
The number of unbalanced interior nodes of divide-and-conquer trees on leaves is known to form a sequence of dilations of the Takagi function on dyadic rationals. We use this fact to derive identities on the Takagi function and on the Hamming weight of an integer in terms of the Takagi function.
Keywords
Cite
@article{arxiv.2111.05996,
title = {Takagi Function Identities on Dyadic Rationals},
author = {Laura Monroe},
journal= {arXiv preprint arXiv:2111.05996},
year = {2024}
}
Comments
11 pages, 1 figure. This paper is a small portion of arXiv:2108.11496 with some additions, split for publication. Version 2 adds references to another proof of the weight theorem and makes some notation changes. Version 3 is the published version