A framework for Coxeter spectral classification of finite posets and their mesh geometries of roots.

DOI10.1155/2013/743734zbMath1284.16018OpenAlexW2016930771WikidataQ58988767 ScholiaQ58988767MaRDI QIDQ1950019

Daniel Simson, Katarzyna Zając

Publication date: 23 May 2013

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/743734

zbMATH Keywords

Coxeter numbersCoxeter matricesCoxeter polynomialsCoxeter spectraclassification of finite posetsmatrix representations of posetspositive semidefinite symmetric Gram matrices

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Representations of quivers and partially ordered sets (16G20) Quadratic and bilinear forms, inner products (15A63) Algebraic aspects of posets (06A11) Canonical forms, reductions, classification (15A21)

Related Items

A Gram classification of non-negative corank-two loop-free edge-bipartite graphs ⋮ Coxeter Invariants for Non-negative Unit Forms of Dynkin Type 𝔸r ⋮ On algorithmic Coxeter spectral analysis of positive posets ⋮ On combinatorial algorithms computing mesh root systems and matrix morsifications for the Dynkin diagram \(\mathbb A_n\) ⋮ A Strong Gram Classification of Non-negative Unit Forms of Dynkin Type 𝔸r ⋮ Coxeter spectral classification of almost \(TP\)-critical one-peak posets using symbolic and numeric computations. ⋮ Structure and a Coxeter-Dynkin type classification of corank two non-negative posets. ⋮ Inflation algorithm for loop-free non-negative edge-bipartite graphs of corank at least two ⋮ On the structure of loop-free non-negative edge-bipartite graphs ⋮ A Coxeter type classification of one-peak principal posets

Uses Software

• Maple
• Python

Cites Work

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