Combinatorial topology and the global dimension of algebras arising in combinatorics

DOI10.4171/JEMS/579zbMath1330.05166arXiv1205.1159OpenAlexW2962746378MaRDI QIDQ907273

Stuart W. Margolis, Benjamin Steinberg, Franco V. Saliola

Publication date: 25 January 2016

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.1159

zbMATH Keywords

classifying spacecohomologyorder complexglobal dimensionchordal graphhyperplane arrangementshereditary algebraleft regular bandLeray number

Mathematics Subject Classification ID

Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Representations of associative Artinian rings (16G10) Homological dimension in associative algebras (16E10) Combinatorial aspects of simplicial complexes (05E45)

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Cites Work

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• Edge flipping in graphs
• On rigid circuit graphs
• Functions of random walks on hyperplane arrangements
• Algebraic properties of edge ideals via combinatorial topology
• Note: random-to-front shuffles on trees
• From shuffling cards to walking around the building: An introduction to modern Markov chain theory
• Random walks and hyperplane arrangements
• Morse theory and finiteness properties of groups
• Semigroups, rings, and Markov chains
• Cohomology of incidence algebras and simplicial complexes
• The classifying space of a bound quiver.
• A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements
• Coxeter groups and Hopf algebras.
• Adjoint functors and derived functors with an application to the cohomology of semigroups
• Combinatorial problems of commutation and rearrangements
• Hereditary and semi-hereditary monoids
• Semigroups admitting relative inverses
• Monoidal Functors, Species and Hopf Algebras
• Algebras and Quadratic Forms
• A Monoid which is Right FP _∞ but not Left FP ₁
• Buildings
• Random Walks, Arrangements, Cell Complexes, Greedoids, and Self-Organizing Libraries
• Combinatorial Stratification of Complex Arrangements