Ehrhart polynomial for lattice squares, cubes and hypercubes

Eugen J. Ionascu

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arXiv · 1508.03643

Ehrhart polynomial for lattice squares, cubes and hypercubes

Eugen J. Ionascu

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Abstract

In this paper we are constructing integer lattice squares, cubes or hypercubes in $\mathbb R^d$ with $d\in \{2,3,4\}$. For squares and cubes we find a complete description of their Ehrhart polynomial. For hypercubes, we compute one of the coefficients and show that there exists a simple linear relation between the other two unknown coefficients. This allows as to formulate a conjecture of what the Ehrhart polynomial is in this case.

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Eugen J. Ionascu. 2015-08-14. Ehrhart polynomial for lattice squares, cubes and hypercubes. https://arxiv.org/abs/1508.03643

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