Minimum shadows in uniform hypergraphs and a generalization of the Takagi function

Peter Frankl, Makoto Matsumoto, Imre Z. Ruzsa, Norihide Tokushige

Research output: Contribution to journalArticle

12 Citations (Scopus)


The shadow function is closely related to the Kruskal-Katona Theorem. The Takagi function is a standard example of a nowhere differentiable continuous function. The purpose of this paper is to exhibit a rather surprising relationship between the shadow function and the Takagi function. Using this relationship, one can approximately compute the size of minimum shadows in uniform hypergraphs with a given number of edges. In order to describe the asymptotic behaviour of the size of shadows, we introduce a new, generalized Takagi function. The results explain the difficulties, often encountered when using the best possible bounds arising from the Kruskal-Katona Theorem.

Original languageEnglish
Pages (from-to)125-148
Number of pages24
JournalJournal of Combinatorial Theory, Series A
Issue number1
Publication statusPublished - Jan 1995


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this