Edge colored hypergraphic arrangements

TL;DR

This paper explores the relationship between edge colored hypergraphs and subspace arrangements, providing a generalized chromatic polynomial and conditions for non-trivial Massey products via spectral sequences.

Contribution

It introduces a new connection between hypergraph colorings and subspace arrangements, and offers a sufficient condition for Massey products using spectral sequence analysis.

Findings

Characteristic polynomial equals a generalized chromatic polynomial

Provides a sufficient condition for non-trivial Massey products

Analyzes spectral sequences of Lie coalgebras

Abstract

A subspace arrangement defined by intersections of hyperplanes of the braid arrangement can be encoded by an edge colored hypergraph. It turns out that the characteristic polynomial of this type of subspace arrangement is given by a generalized chromatic polynomial of the associated edge colored hypergraph. The main result of this paper supplies a sufficient condition for the existence of non-trivial Massey products of the subspace arrangements complex complement. This is accomplished by studying a spectral sequence associated to the Lie coalgebras of Sinha and Walter.