Consequences of the packing problem

Alexandra Seceleanu; Benjamin Drabkin; Brendan Williams; Caleb Fong; Hrishikesh Bodas; Justin Kim; Su Jin; Tingting Tang; Wenxuan Li

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Consequences of the packing problem

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arxiv 2101.04010 v2 pith:EH4RDXBN submitted 2021-01-11 math.AC math.CO

Hrishikesh Bodas , Benjamin Drabkin , Caleb Fong , Su Jin , Justin Kim , Wenxuan Li , Alexandra Seceleanu , Tingting Tang

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Brendan Williams

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keywords consequencespackingproblemadditionalalgebraiccombinatorialconjectureconjectures

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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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