One-peak posets with positive quadratic Tits form, their mesh translation quivers of roots, and programming in Maple and Python

DOI10.1016/j.laa.2011.10.045zbMath1272.06009OpenAlexW1987885619WikidataQ113293673 ScholiaQ113293673MaRDI QIDQ2427915

Daniel Simson, Marcin Gąsiorek

Publication date: 19 April 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.10.045

zbMATH Keywords

posetquadratic formreflectionsMapleDynkin diagramsrootCoxeter polynomialPythonmesh quiverbilinear Tits form

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Combinatorics of partially ordered sets (06A07) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Representations of quivers and partially ordered sets (16G20) Quadratic and bilinear forms, inner products (15A63) Computational aspects of associative rings (general theory) (16Z05) Algebraic aspects of posets (06A11)

Related Items

A Gram classification of non-negative corank-two loop-free edge-bipartite graphs, On algorithmic Coxeter spectral analysis of positive posets, On combinatorial algorithms computing mesh root systems and matrix morsifications for the Dynkin diagram \(\mathbb A_n\), Systems of subspaces of a unitary space, On the transitivity coefficients for minimal posets with nonpositive quadratic Tits form, A framework for Coxeter spectral classification of finite posets and their mesh geometries of roots., Coxeter spectral classification of almost \(TP\)-critical one-peak posets using symbolic and numeric computations., On mesh geometries of root Coxeter orbits and mesh algorithms for corank two edge-bipartite signed graphs, Structure and a Coxeter-Dynkin type classification of corank two non-negative posets., Applications of matrix morsifications to Coxeter spectral study of loop-free edge-bipartite graphs, Applications of mesh algorithms and self-dual mesh geometries of root Coxeter orbits to a Horn-Sergeichuk type problem, Tame-wild dichotomy of Birkhoff type problems for nilpotent linear operators., A Coxeter type classification of one-peak principal posets, Congruence of rational matrices defined by an integer matrix, On Coxeter type study of non-negative posets using matrix morsifications and isotropy groups of Dynkin and Euclidean diagrams., Numeric and mesh algorithms for the Coxeter spectral study of positive edge-bipartite graphs and their isotropy groups

Uses Software

• Maple
• Python

Cites Work

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