Geodesic
On a characterization of lattice cubes via discrete isoperimetric inequalities
David Iglesias ; Eduardo Lucas1
1Universidad de Murcia
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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We obtain a characterization of lattice cubes as the only sets that reach equality in several discrete isoperimetric-type inequalities associated with the $L_{\infty}$ norm, including well-known results by Radcliffe and Veomett. We furthermore provide a new isoperimetric inequality for the lattice point enumerator that generalizes previous results, and for which the aforementioned characterization also holds.
DOI : 10.37236/11024
Classification : 52C07, 11H06
Mots-clés : discrete isoperimetric-type inequalities, lattice cubes

David Iglesias    ; Eduardo Lucas  1

1 Universidad de Murcia 
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David Iglesias; Eduardo Lucas. On a characterization of lattice cubes via discrete isoperimetric inequalities. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11024

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