English

On Dedekind's problem for complete simple games

Combinatorics 2010-01-19 v1

Abstract

We combine the parametric Barvinok algorithm with a generation algorithm for a finite list of suitably chosen discrete sub-cases on the enumeration of complete simple games, i.e. a special subclass of monotone Boolean functions. Recently, Freixas et al. have proven an enumeration formula for complete simple games with two types of voters. We will provide a shorter proof and an enumeration formula for complete simple games with two shift-minimal winning coalitions.

Keywords

Cite

@article{arxiv.1001.3045,
  title  = {On Dedekind's problem for complete simple games},
  author = {Sascha Kurz and Nikolas Tautenhahn},
  journal= {arXiv preprint arXiv:1001.3045},
  year   = {2010}
}

Comments

13 pages, 1 figure, 6 tables, submitted to ISSAC 2010

R2 v1 2026-06-21T14:36:04.859Z