Geodesic
Bounds on area involving lattice size
Jenya Soprunova1
1Kent State University
The electronic journal of combinatorics, Tome 30 (2023) no. 4
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The lattice size of a lattice polygon $P$ is a combinatorial invariant of $P$ that was recently introduced in relation to the problem of bounding the total degree and the bi-degree of the defining equation of an algebraic curve. In this paper, we establish sharp lower bounds on the area of plane convex bodies $P\subset\mathbb{R}^2$ that involve the lattice size of $P$. In particular, we improve bounds given by Arnold, and Bárány and Pach. We also provide a classification of minimal lattice polygons $P\subset\mathbb{R}^2$ of fixed lattice size ${\operatorname{ls_\square}}(P)$.
DOI : 10.37236/11296
Classification : 52B20, 52C05, 11H06
Mots-clés : convex body, lattice size, lattice polygon

Jenya Soprunova  1

1 Kent State University 
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Jenya Soprunova. Bounds on area involving lattice size. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11296

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