A Hilton-Milner theorem for exterior algebras

TL;DR

This paper extends classical combinatorial theorems, specifically the Hilton-Milner theorem, to the setting of exterior algebras, building on recent work that generalized Erdős-Ko-Rado results to subspaces of forms.

Contribution

It provides a new extension of the Hilton-Milner theorem within exterior algebras, addressing a question posed by recent researchers.

Findings

Established a Hilton-Milner type theorem for exterior algebras

Extended combinatorial bounds to algebraic structures

Answered a specific open question in the field

Abstract

Recent work of Scott and Wilmer and of Woodroofe extends the Erd\H{o}s-Ko-Rado theorem from set systems to subspaces of k-forms in an exterior algebra. We prove an extension of the Hilton-Milner theorem to the exterior algebra setting, answering in a strong way a question asked by these authors.