Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\)

• Date: 2026
• Main Author: Gąsiorek, Marcin
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: non-negative poset; unit quadratic form; Coxeter-Dynkin type; Coxeter spectrum; 06A07; 06A11; 11E04; 68W30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2408
• Journal Title: Algebra and Discrete Mathematics

We give a complete description of connected non-negative Dynkin type Dyn\(_I=\mathbb{E}_m\) posets and prove that the number of such posets is finite. Moreover, by means of computer assisted analysis, we give a complete Coxeter classification of this class and prove that the pair (Dyn\(_I=\mathbb{E}...