Counterexamples to Siegel's Conjecture
Kean P. Fallon, Madisyn Janusiak, Edward D. Kim, Avery McLain
TL;DR
This paper demonstrates that the intersection of a Hirsch polytope and a cube can result in a non-Hirsch polytope, providing counterexamples to Siegel's conjecture.
Contribution
It presents explicit counterexamples showing that the intersection of a Hirsch polytope and a cube need not be Hirsch, challenging previous assumptions.
Findings
Counterexamples to Siegel's conjecture.
Intersection of Hirsch polytope and cube can be non-Hirsch.
Challenges existing beliefs about polytope intersections.
Abstract
We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Analytic Number Theory Research