Spectrum for first-order properties of random hypergraphs

TL;DR

This paper explores the spectrum of first-order properties in random hypergraphs, analyzing its characteristics, bounds, and limit points, extending concepts from random graphs to hypergraphs.

Contribution

It introduces the spectrum concept for first-order properties in hypergraphs and provides bounds and analysis of its key features, a novel extension from graph theory.

Findings

Spectrum bounds for hypergraph properties established

Limit points of the spectrum characterized

Minimum value of the spectrum's limit set estimated

Abstract

The notion of spectrum of first-order properties introduced by J. Spencer for Erdos-Renyi random graph is considered in relation to random uniform hypergraphs. We study properties of spectrum for first-order formulae with bounded quantifier depth and estimate the values of minimum and maximum points of this spectrum. We also consider the set of limit points of the spectrum and give a bound for its minimum value.