Generalized Rank Functions and an Entropy Argument

Jeff Kahn, Alexander Lawrenz

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A rank function is a function f:2[d]→N such that f()=0 and f(A)≤ f(A∪x)≤f(A)+1 for all A⊆[d], x∈[d]\A. Athanasiadis conjectured an upper bound on the number of rank functions on 2[d]. We prove this conjecture and generalize it to functions with bounded jumps.

Original languageEnglish (US)
Pages (from-to)398-403
Number of pages6
JournalJournal of Combinatorial Theory. Series A
Volume87
Issue number2
DOIs
StatePublished - Aug 1999

All Science Journal Classification (ASJC) codes

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

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