Skip to content
DraconiticResearch
Search Sources API
182,549 studies31 sourcesUpdated 19 min ago
PreprintCC BY 4.0arXiv

Real-rooted Ehrhart h*-polynomials of crown posets and wheel and whirl matroids

  • Ying Cao
  • Houshan Fu
Open at sourcePDFDOICite

Abstract

We prove that the Ehrhart h*-polynomials of crown order polytopes are real-rooted, settling a conjecture of Lundström and Saud Maia Leite. For each integer r≥3, the crown order polytope on 2r elements and the rank-r whirl base polytope have the same h*-polynomial. The h*-polynomials of the rank-r wheel and whirl base polytopes, as well as every convex combination of the two, have 2r−2 distinct negative roots. Their coefficient sequences are positive, unimodal, and strictly ultra log-concave of order 2r−2.

Related

  1. Ehrhart positivity for lattice path matroids
    Luis Ferroni, Alejandro H. Morales, Greta Panova
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. Embedding rooted blow-ups of tree posets
    Balázs Patkós
    arXivPreprintCC BY-NC-ND 4.0Full textCombinatorics & discrete mathematicsarXiv
  3. Ehrhart polynomials of cyclic polytopes as averages of zonotope Ehrhart polynomials
    Masato Konoike
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. Ehrhart quasi-polynomials with finite abelian congruence constraints
    Aleksander Zujev, Matthew Hudelson
    HALPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsHAL
  5. Palindromic real-rooted polynomials and h-vectors of polytopes
    Peter L. Guo, Mingyang Kang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{cao2026realrooted,
  title = {{Real-rooted Ehrhart $h^*$-polynomials of crown posets and wheel and whirl matroids}},
  author = {Ying Cao and Houshan Fu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40496},
  eprint = {2610.40496},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40496},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Real-rooted Ehrhart h^*-polynomials of crown posets and wheel and whirl matroids
AU  - Ying Cao
AU  - Houshan Fu
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40496
UR  - https://arxiv.org/abs/2610.40496
AB  - We prove that the Ehrhart h^*-polynomials of crown order polytopes are real-rooted, settling a conjecture of Lundström and Saud Maia Leite. For each integer r≥3, the crown order polytope on 2r elements and the rank-r whirl base polytope have the same h^*-polynomial. The h^*-polynomials of the rank-r wheel and whirl base polytopes, as well as every convex combination of the two, have 2r−2 distinct negative roots. Their coefficient sequences are positive, unimodal, and strictly ultra log-concave of order 2r−2.
ER  -