On Algorithmic Study of Non-negative Posets of Corank at Most Two and their Coxeter-Dynkin Types

DOI10.3233/FI-2015-1238zbMath1335.05171OpenAlexW1010616232MaRDI QIDQ2805472

Katarzyna Zając, Marcin Gąsiorek

Publication date: 11 May 2016

Published in: Fundamenta Informaticae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3233/fi-2015-1238

zbMATH Keywords

posetDynkin diagramCoxeter spectrumCoxeter-Dynkin type

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Combinatorics of partially ordered sets (06A07) Graph algorithms (graph-theoretic aspects) (05C85)

Related Items (14)

A Gram classification of non-negative corank-two loop-free edge-bipartite graphs ⋮ A Gram classification of principal Cox-regular edge-bipartite graphs via inflation algorithm ⋮ On algorithmic Coxeter spectral analysis of positive posets ⋮ Symbolic computation of strong Gram congruences for Cox-regular positive edge-bipartite graphs with loops ⋮ On mesh geometries of root Coxeter orbits and mesh algorithms for corank two edge-bipartite signed graphs ⋮ A Coxeter spectral classification of positive edge-bipartite graphs. II: Dynkin type \(\mathbb{D}_n\) ⋮ Structure and a Coxeter-Dynkin type classification of corank two non-negative posets. ⋮ Applications of mesh algorithms and self-dual mesh geometries of root Coxeter orbits to a Horn-Sergeichuk type problem ⋮ 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 spectral classification of positive edge-bipartite graphs. I: Dynkin types \(\mathcal{B}_n\), \(\mathcal{C}_n\), \(\mathcal{F}_4\), \(\mathcal{G}_2\), \(\mathbb{E}_6\), \(\mathbb{E}_7\), \(\mathbb{E}_8\) ⋮ 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.

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