Takagi Function Identities on Dyadic Rationals

Autor:	Monroe, Laura
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics Computer Science - Data Structures and Algorithms Mathematics - Classical Analysis and ODEs Mathematics - Number Theory 68R05 (Primary) 26A27 (Secondary) 05C05 28A80
Zdroj:	Journal of Integer Sequences, Vol. 27 (2024), Article 24.2.7
Druh dokumentu:	Working Paper
Popis:	The number of unbalanced interior nodes of divide-and-conquer trees on $n$ 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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.05996 Zobrazit plný text záznamu View this record from Arxiv