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PreprintCC BY 4.0arXiv

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 1≤ k<⌊n/2⌋, 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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Cite

BibTeXRIS
BibTeX
@misc{chen2026magic,
  title = {{On the magic positivity of the Ehrhart polynomials of dilated base polytope of minimal matroid}},
  author = {Jiaxuan Chen and Chance Crigler and Shengtao Ding and Dana Paquin and Julian Schennach},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32050},
  eprint = {2610.32050},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32050},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the magic positivity of the Ehrhart polynomials of dilated base polytope of minimal matroid
AU  - Jiaxuan Chen
AU  - Chance Crigler
AU  - Shengtao Ding
AU  - Dana Paquin
AU  - Julian Schennach
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32050
UR  - https://arxiv.org/abs/2610.32050
AB  - 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 1≤ k<⌊n/2⌋, 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.
ER  -