Algorithmic computation of principal posets using Maple and Python

• Date: 2018
• Main Authors: Gąsiorek, Marcin, Simson, Daniel, Zając, Katarzyna
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: principal poset; edge-bipartite graph; unit quadratic form; computer algorithm; Gram matrix; Coxeter polynomial; Coxeter spectrum; 06A11; 15A63; 68R05; 68W30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1023
• Journal Title: Algebra and Discrete Mathematics

We present symbolic and numerical algorithms for a computer search in the Coxeter spectral classification problems. One of the main aims of the paper is to study finite posets \(I\) that are principal, i.e., the rational symmetric Gram matrix \(G_I : = \frac{1}{2}[C_I+ C^{tr}_I]\in\mathbb{M_I(\mathb...