Groupoids, root systems and weak order II

Keywords

Root (linguistics), Order (exchange), Mathematics, Economics, Philosophy

References

• Combinatorics of Coxeter GroupsBailee Zacovic — 2005
• On rigidity of abstract root systems of Coxeter systemsMatthew Dyer — 2010
• Semidirect Product Decomposition of Coxeter GroupsCédric Bonnafé, Matthew Dyer — 2008
• Reflection subgroups of Coxeter systemsMatthew Dyer — 1990
• Powers of Coxeter elements in infinite groups are reducedDavid E Speyer — 2007
• Hyperplane arrangements with a lattice of regionsAnders Björner, Paul H. Edelman, Günter M. Ziegler — 1990
• NORMALIZERS OF PARABOLIC SUBGROUPS OF COXETER GROUPSDaniel Allcock — 2011
• Eléments de MathématiqueNicolás Bourbaki — 1964
• Embeddings of root systems II: Permutation root systemsMatthew Dyer — 2009
• Elementary roots and admissible subsets of Coxeter groupsMatthew Dyer — 2009
• Embeddings of root systems I: Root systems over commutative ringsMatthew Dyer — 2009
• Normalizers of Parabolic Subgroups of Reflection GroupsRobert B. Howlett — 1980
• Weyl groupoids with at most three objectsMichael Cuntz, I. Heckenberger — 2008
• Large convex sets in oriented matroidsJ Büchi, William E. Fenton — 1988
• Systèmes de racines sur un anneau commutatif totalement ordonnéJean-Yves Hée — 1991
• A generalization of Coxeter groups, root systems, and Matsumoto’s theoremI. Heckenberger, Hiroyuki Yamane — 2006
• On the root system of a coxeter groupVinay V. Deodhar — 1982
• The Cycle Space of an Infinite GraphReinhard Diestel — 2005
• On Normal Subgroups of Coxeter Groups Generated by Standard Parabolic SubgroupsŚwiatosław R. Gal — 2005
• Geometric combinatorics of Weyl groupoidsI. Heckenberger, Volkmar Welker — 2010

Cited by

• On inversion sets and the weak order in Coxeter groupsChristophe Hohlweg, Jean‐Philippe Labbé — 2015
• On the Weak Order of Orthogonal GroupsAnnette Pilkington — 2011
• Groupoids with root systems in real vector spacesTimothy Ferdinands — 2015
• A characterization of simplicial oriented geometries as groupoids with root systems.Matthew Dyer, Weijia Wang — 2019
• Extending the weak order on Coxeter groupsFrançois Viard — 2020
• Coxeter systems, left inversion sets, and higher dimensional cubesHarrison Gimenez — 2025

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