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arXiv · 2610.32050

On the magic positivity of the Ehrhart polynomials of dilated base polytope of minimal matroid

Jiaxuan Chen·Chance Crigler·Shengtao Ding·Dana Paquin·Julian Schennach
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Abstract

In this paper, we consider the magic positivity of the Ehrhart polynomial of dilated base polytope of minimal matroid of rank $k$ dimension $n$. We prove that for $\displaystyle 1\leq k<\lfloor\frac{n}{2}\rfloor$, the $n-k-1$ dilate of the Ehrhart polynomial is not magic positive. We also show that for sufficiently large $n$, the $n-k$ dilate of the Ehrhart polynomial is, in general, magic positive. This gives rise to a lower bound of the $m-$index of the Ehrhart polynomial.

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Jiaxuan Chen, Chance Crigler, Shengtao Ding, Dana Paquin, Julian Schennach. 2026-10-23. On the magic positivity of the Ehrhart polynomials of dilated base polytope of minimal matroid. https://arxiv.org/abs/2610.32050

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