Skip to content
DraconiticResearch
Search Sources API
186,546 studies31 sourcesUpdated 42 min ago
Peer-reviewedCC BY 4.0Algebraic Combinatorics

On chain polynomials of geometric lattices

  • Petter Brändén1
  • Leonardo Saud Maia Leite1
  1. 1KTH Royal Institute of Technology, Department of Mathematics, SE-100 44 Stockholm (Sweden)
Open at sourcePDFDOICite

Abstract

Athanasiadis and Kalampogia-Evangelinou recently conjectured that the chain polynomial of any geometric lattice has only real zeros. We verify this conjecture for families of geometric lattices including perfect matroid designs, Dowling lattices, and for a class of geometric lattices that contains all lattices of flats of paving matroids.

We also investigate how the conjecture behaves with respect to certain operations such as direct products, ordinal sums and single-element extensions.

Related

  1. Norm attainment for multilinear operators and polynomials on Banach Spaces and Banach lattices
    Luis A. Garcia, José Lucas P. Luiz, Vinícius C. C. Miranda
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Chow polynomials and chain polynomials of matroids are not log-concave
    Gergely Bérczi, Basile Coron, Christopher Eur +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Gauss Circle Lattices with Geometric Convolutions for Synthesizing High Dimensional Image-Source Room Impulse Responses
    Yuancheng Luo
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. Real stability of layer-refined antichain polynomials for three-chain products with a two-element factor
    Weiqi Jiang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  5. The geometric combinatorics of k-shuffle polynomials
    Chloé Postel-Vinay
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@article{branden2026chain,
  title = {{On chain polynomials of geometric lattices}},
  author = {Petter Brändén and Leonardo Saud Maia Leite},
  journal = {Algebraic Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.5802/alco.513},
  url = {https://alco.centre-mersenne.org/articles/10.5802/alco.513/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - On chain polynomials of geometric lattices
AU  - Petter Brändén
AU  - Leonardo Saud Maia Leite
PY  - 2026
DA  - 2026/10/27
JO  - Algebraic Combinatorics
DO  - 10.5802/alco.513
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.513/
AB  - Athanasiadis and Kalampogia-Evangelinou recently conjectured that the chain polynomial of any geometric lattice has only real zeros. We verify this conjecture for families of geometric lattices including perfect matroid designs, Dowling lattices, and for a class of geometric lattices that contains all lattices of flats of paving matroids.  We also investigate how the conjecture behaves with respect to certain operations such as direct products, ordinal sums and single-element extensions.
SN  - 2589-5486
ER  -