Faber-Harris Conjecture on the Isolation Lemma

For an inclusion-free hypergraph on $n$ vertices, a weight assignment $w:[n]\to[d]$ is isolating when a unique edge attains minimum weight. Faber and Harris conjectured that the number of isolating assignments is at least $n\sum_{j=0}^{d-1} j^{n-1}$, attained by the hypergraph of $n$ singleton edges. The bound holds, and extends to a more general class of objective functions.

Result

Proved

Status

Resolved

AI contribution

AI co-developed

Method

Argument

Field

Extremal combinatorics

Posed by

Vance Faber, David G. Harris

Year posed

2018

Years open

8y

Solved

2026-07-07

Model

ChatGPT

Vendor

OpenAI

Collaborators

Vance Faber, David G. Harris

Verification

Unreviewed

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article