Consequences of the packing problem
Hrishikesh Bodas, Benjamin Drabkin, Caleb Fong, Su Jin, Justin Kim,, Wenxuan Li, Alexandra Seceleanu, Tingting Tang, Brendan Williams
TL;DR
This paper investigates the implications of the unresolved packing problem in combinatorial optimization by analyzing algebraic invariants, confirming some consequences and raising new questions.
Contribution
It establishes the validity of certain consequences of the packing problem using algebraic invariants, despite the conjecture remaining unresolved.
Findings
Confirmed the validity of some consequences of the packing problem
Presented new questions and conjectures related to the packing problem
Used algebraic invariants of square-free monomial ideals in the analysis
Abstract
We study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals. While the packing problem is currently unresolved, we successfully settle the validity of its consequences. Our work prompts additional questions and conjectures, which are presented together with their motivation.
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