Weighted model sets and their higher point-correlations

TL;DR

This paper explores weighted model sets, demonstrating that different configurations can share identical higher-order point correlations, which has implications for understanding their structural properties.

Contribution

It introduces examples of weighted model sets with identical multi-point correlations, highlighting the complexity of their structural characterization.

Findings

Different weighted model sets can have the same 2-5 point correlations

Higher point correlations do not uniquely determine the structure

Examples challenge assumptions about correlation-based identification

Abstract

Examples of distinct weighted model sets with equal 2, 3, 4, 5-point correlations are given.