1. Lattice Polygons and the Number 2i + 7.
- Author
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Haase, Christian and Schicho, Josef
- Subjects
- *
ALGEBRAIC geometry , *TORIC varieties , *MATHEMATICAL inequalities , *ALGEBRAIC curves , *LATTICE theory , *POLYGONS , *MATHEMATICAL proofs , *POLYNOMIALS , *ALGEBRAIC varieties , *MATHEMATICAL analysis - Abstract
The article provides information on the inequalities of lattice polygons in relation to Scott's inequality and the equation 2i + 7. It states that algebraic geometry is used to study lattice equivalent polygons, since toric geometry is a powerful link that connects discrete and algebraic geometry. Moreover, the proposition b ⩽ 2i + 7 is proven using Pick's Theorem with three equivalent inequalities. Furthermore, Scott's proof indicates that (x,y) = (3,3) is the only point where both upper bounds reach zero and the only case where equality can hold in Onion-Skin Theorem.
- Published
- 2009
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