Rectangular groupoids and related structures

DOI10.1016/j.disc.2013.03.012zbMath1283.08011OpenAlexW2092755250WikidataQ42111344 ScholiaQ42111344MaRDI QIDQ392631

Tim Boykett

Publication date: 15 January 2014

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2013.03.012

zbMATH Keywords

dualitiestransversalsisotopysubvarietiesquasivarietiesgroupoidsgeneral algebramatrix identitiespath property

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Quasivarieties (08C15) Sets with a single binary operation (groupoids) (20N02)

Related Items (4)

Simplicial complexes and closure systems induced by indistinguishability relations ⋮ Pairings and related symmetry notions ⋮ Welch sets for random generation and representation of reversible one-dimensional cellular automata ⋮ Local dissymmetry on graphs and related algebraic structures

Cites Work

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• On rational circulants satisfying \(A^ m=dI+\lambda J\)
• Orderly algorithm to enumerate central groupoids and their graphs
• On the matrix equation \(A^m=\lambda J\)
• Directed graphs with unique paths of fixed length
• \(g\)-circulant solutions to the (0,1) matrix equation \(A^m=J_n\)
• On the existence of finite central groupoids of all possible ranks. I
• Central groupoids, central digraphs, and zero-one matrices \(A\) satisfying \(A^{2}=J\).
• On the g-circulant solutions to the matrix equation \(A^m=\lambda J\)
• Efficient exhaustive listings of reversible one dimensional cellular automata
• A generalization of the matrix equation \(A^ 2=J\)
• Notes on central groupoids
• Products of Points--Some Simple Algebras and their Identities
• Idempotent Semigroups
• Reconstruction of group multiplication tables by quadrangle criterion

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