Counting polygon spaces, Boolean functions and majority games

TL;DR

This paper reveals a surprising connection between the classification of polygon spaces and the enumeration of certain classes of Boolean functions and majority games, highlighting deep combinatorial relationships.

Contribution

It establishes a novel correspondence between polygon space classifications and self-dual threshold functions, unifying geometric and Boolean combinatorial concepts.

Findings

Numbers in polygon space classification match counts of self-dual threshold functions.

Identifies a link between geometric configurations and Boolean function classes.

Provides a unified framework connecting geometry and combinatorics.

Abstract

We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.