Year: 2026
Type: preprint
Abstract: We disprove a weighted generalization of the union-set conjecture [Fra95] raised in [Gow16]. We construct nonnegative weights on subsets of a finite ground set satisfying $w(\varnothing)=0$ and $w(A\cup B)\ge\min\{w(A),w(B)\}$, while every coordinate belongs to an arbitrarily small fraction of the total weight.
Source: arXiv (Cornell University)
Author: Wang, Yimeng
Institution: University of California, Los Angeles
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214099221