Work

The Hilton-Milner theorem in the $\ell_2$-norm

Year: 2026

Type: preprint

Abstract: The Hilton-Milner theorem is a classical theorem in extremal set theory which determines the maximum size of a nontrivial $k$-uniform intersecting family. In this paper, we prove an exact version of the Hilton-Milner theorem in the $\ell_2$-norm. Our method also gives an asymptotic version of the Hilton-Milner theorem in the $(j, p)$-norm.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.12433

Authors: Brooks, George, Linz, William

Institutions: University of South Carolina, University of Memphis

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: RTG: Mathematical Foundation of Data Science at University of South Carolina

OpenAlex ID: W7221082616

Cites: 3

Cited by:

Related to: 10