Families of Polytopes with Rational Linear Precision in Higher Dimensions

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Davies, I (Author) Other; Duarte, E (Author) FCUP; Portakal, I (Author) Other; Sorea, MS (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

ISSN: 1615-3375

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Other information

Authenticus ID: P-00X-28P

DOI: 10.1007/s10208-022-09583-7

Abstract (EN): In this article, we introduce a new family of lattice polytopes with rational linear precision. For this purpose, we define a new class of discrete statistical models that we call multinomial staged tree models. We prove that these models have rational maximum likelihood estimators (MLE) and give a criterion for these models to be log-linear. Our main result is then obtained by applying Garcia-Puente and Sottile's theorem that establishes a correspondence between polytopes with rational linear precision and log-linear models with rational MLE. Throughout this article, we also study the interplay between the primitive collections of the normal fan of a polytope with rational linear precision and the shape of the Horn matrix of its corresponding statistical model. Finally, we investigate lattice polytopes arising from toric multinomial staged tree models, in terms of the combinatorics of their tree representations.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 52