Castillo, Federico et Labbé, Jean-Philippe.
2025.
« Lineup polytopes of products of simplices ».
Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions, vol. 12, nº 4.
pp. 787-818.
Prévisualisation |
PDF
Labbe-JP-2025-32584.pdf - Version publiée Licence d'utilisation : Creative Commons CC BY. Télécharger (818kB) | Prévisualisation |
Résumé
Consider a real point configuration A of size n and an integer r < n. The vertices of the r-lineup polytope of A correspond to the possible orderings of the top r points of the configuration obtained by maximizing a linear functional. The motivation behind the study of lineup polytopes comes from the representability problem in quantum chemistry. In that context, the relevant point configurations are the vertices of hypersimplices and the integer points contained in an inflated regular simplex. The central problem consists in providing an inequality representation of lineup polytopes as efficiently as possible. In this article, we adapt the developed techniques to the quantum information theory setup. The appropriate point configurations become the vertices of products of simplices. A particular case is that of lineup polytopes of cubes, which form a type B analog of hypersimplices, where the symmetric group of type A naturally acts. To obtain the inequalities, we center our attention on the combinatorics and the symmetry of products of simplices to obtain an algorithmic solution. Along the way, we establish relationships between lineup polytopes of products of simplices with the Gale order, standard Young tableaux, and the resonance arrangement.
| Type de document: | Article publié dans une revue, révisé par les pairs |
|---|---|
| Professeur: | Professeur Labbé, Jean-Philippe |
| Affiliation: | Département des enseignements généraux |
| Date de dépôt: | 23 oct. 2025 13:57 |
| Dernière modification: | 14 nov. 2025 19:47 |
| URI: | https://espace2.etsmtl.ca/id/eprint/32584 |
Actions (Authentification requise)
 |
Dernière vérification avant le dépôt |