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Deformation cones of Tesler polytopes

  • Yonggyu Lee and Fu Liu EMAIL logo
Published/Copyright: April 26, 2024
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Advances in Geometry
From the journal Advances in Geometry Volume 24 Issue 2

Abstract

For a ∈ R≥0n , the Tesler polytope Tesn(a) is the set of upper triangular matrices with non-negative entries whose hook sum vector is a. We first give a different proof of the known fact that for every fixed a0 ∈ R>0n , all the Tesler polytopes Tesn(a) are deformations of Tesn(a0). We then calculate the deformation cone of Tesn(a0). In the process, we also show that any deformation of Tesn(a0) is a translation of a Tesler polytope. Lastly, we consider a larger family of polytopes called flow polytopes which contains the family of Tesler polytopes and chracterize the flow polytopes which are deformations of Tesn(a0).

Keywords: Tesler polytope; deformation cone
MSC 2010: 52B20

Funding statement: The second author is partially supported by a grant from the Simons Foundation #426756 and an NSF grant #2153897-0.

Acknowledgements

We are grateful to the two anonymous referees for their valuable comments and suggestions. In particular, we thank one of the referees who brought to our attention the result stated in Theorem 3.9, which was not in a previous version of this article.

  1. Communicated by: M. Joswig

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Received: 2023-01-02
Revised: 2023-11-11
Published Online: 2024-04-26
Published in Print: 2024-04-25

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Inequalities for f*-vectors of lattice polytopes
  3. Lower bound on the translative covering density of octahedra
  4. Variations on the Weak Bounded Negativity Conjecture
  5. Poisson Structures on moduli spaces of Higgs bundles over stacky curves
  6. Generalized Shioda–Inose structures of order 3
  7. Deformation cones of Tesler polytopes
  8. Some observations on conformal symmetries of G2-structures
  9. Characterization of the sphere and of bodies of revolution by means of Larman points
  10. Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
  11. The feet of orthogonal Buekenhout–Metz unitals
https://doi.org/10.1515/advgeom-2024-0003
Keywords for this article
Tesler polytope; deformation cone

Articles in the same Issue

  1. Frontmatter
  2. Inequalities for f*-vectors of lattice polytopes
  3. Lower bound on the translative covering density of octahedra
  4. Variations on the Weak Bounded Negativity Conjecture
  5. Poisson Structures on moduli spaces of Higgs bundles over stacky curves
  6. Generalized Shioda–Inose structures of order 3
  7. Deformation cones of Tesler polytopes
  8. Some observations on conformal symmetries of G2-structures
  9. Characterization of the sphere and of bodies of revolution by means of Larman points
  10. Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
  11. The feet of orthogonal Buekenhout–Metz unitals
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