English

Local Maxima of Quadratic Boolean Functions

Combinatorics 2019-02-20 v1

Abstract

How many strict local maxima can a real quadratic function on {0,1}n\{0,1\}^n have? Holzman conjectured a maximum of (nn/2)n \choose \lfloor n/2 \rfloor. The aim of this paper is to prove this conjecture. Our approach is via a generalization of Sperner's theorem that may be of independent interest.

Cite

@article{arxiv.1310.1570,
  title  = {Local Maxima of Quadratic Boolean Functions},
  author = {Hunter Spink},
  journal= {arXiv preprint arXiv:1310.1570},
  year   = {2019}
}

Comments

6 pages, 1 figure

R2 v1 2026-06-22T01:41:10.497Z