- On the path homology of Cayley digraphs and covering digraphs
2023/05/31 by Shaobo Di, Sergei O. Ivanov, Lev Mukoseev +1 · 5 citations
Computer Science · Mathematics · #Algorithm #Amino acid #Cayley graph #Cellular homology #Cohomology #Combinatorics #Computation #Digraph #Discrete mathematics #Genetics #Geometric and Algebraic Topology #Graph #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Mayer–Vietoris sequence #Pure mathematics #Relative homology #Simplicial complex #Simplicial homology #Singular homology #Topological and Geometric Data Analysis #Topology (electrical circuits) #math.AT
- Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formula
2023/06/01 by Kirill Brilliantov, Brilliantov, Kirill, Fedor Pavutnitskiy +5 · 1 citation
Computer Science · Mathematics · #Abstract simplicial complex #Algebra over a field #Algebraic Topology (math.AT) #Algebraic number #Algebraic topology #Combinatorics #Computer science #Discrete mathematics #FOS: Computer and information sciences #FOS: Mathematics #Group (periodic table) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Intersection (aeronautics) #Machine Learning (cs.LG) #Mathematics #Natural Language Processing Techniques #Pure mathematics #Simplicial approximation theorem #Simplicial complex #Simplicial set #Theoretical computer science #Topological and Geometric Data Analysis #Topology (electrical circuits)
- Network Geometry and Complexity
2017/11/30 by Daan Mulder, Ginestra Bianconi · 14 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Complex network #Convex geometry #Convex optimization #Convex set #Dimension (graph theory) #Discrete geometry #Gene Regulatory Network Analysis #Geometry #Mathematics #Opinion Dynamics and Social Influence #Order (exchange) #Polyhedron #Polytope #Regular polygon #Simplicial complex #Tetrahedron #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech #gr-qc #physics.soc-ph
- Yoneda Lemma for Simplicial Spaces
2017/11/08 by Nima Rasekh, Rasekh, Nima · 2 citations
Mathematics · #Abstract simplicial complex #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #Computer science #Covariant transformation #FOS: Mathematics #Geometry #Homotopy and Cohomology in Algebraic Topology #Lemma (botany) #Mathematics #Model category #Pure mathematics #Simplicial complex #Simplicial manifold #Simplicial set #Space (punctuation) #h-vector #math.AT #math.CT
- The EKR property for flag pure simplicial complexes without boundary
2017/10/31 by Jorge Olarte, Jorge Alberto Olarte, Francisco Santos +2 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Boundary (topology) #Combinatorics #Commutative Algebra and Its Applications #Conjecture #Dimension (graph theory) #Flag (linear algebra) #Mathematical analysis #Mathematics #Property (philosophy) #Pure mathematics #Simplicial complex #Topological and Geometric Data Analysis #h-vector #math.CO #msc:05C35 #msc:05D05 #msc:05E45
- Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes
2016/02/29 by Owen T. Courtney, Ginestra Bianconi · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Abstract simplicial complex #Bioinformatics and Genomic Networks #Combinatorics #Complex Network Analysis Techniques #Mathematics #Model category #Pure mathematics #Simplicial approximation theorem #Simplicial complex #Simplicial homology #Simplicial manifold #Simplicial set #Topological and Geometric Data Analysis #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech #h-vector #physics.soc-ph
- Simplicial arrangements with up to 27 lines
2011/08/15 by Michael Cuntz, Cuntz, Michael · 2 citations
Engineering · Mathematics · #52C30 #Abstract simplicial complex #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics #Combinatorics (math.CO) #Conjecture #Crystallography #FOS: Mathematics #Isomorphism (crystallography) #Mathematics #Pure mathematics #Simplicial approximation theorem #Simplicial complex #Simplicial manifold #Simplicial set #graph theory and CDMA systems #h-vector #math.CO #msc:52C30
- Digital topological method for computing genus and the Betti numbers
2010/04/16 by Li Chen, Yongwu Rong · 1 citation
Computer Science · Mathematics · #Adjacency list #Artificial intelligence #Betti number #Combinatorics #Computational topology #Computer science #Digital Image Processing Techniques #Digital geometry #Digital image #Digital topology #General topology #Genus #Geometry #Homology (biology) #Image (mathematics) #Image processing #Mathematics #Medical Image Segmentation Techniques #Pure mathematics #Simplicial complex #Singular homology #Surface (topology) #Topological and Geometric Data Analysis #Topological space #Topology (electrical circuits)
- A catalogue of simplicial arrangements in the real projective plane
2009/02/27 by Branko Grünbaum · 2 citations
Engineering · Computer Science · Mathematics · #graph theory and CDMA systems #Graph Labeling and Dimension Problems #Advanced Combinatorial Mathematics #Simplicial complex #Mathematics #Pencil (optics) #Simplicial homology #Simplicial approximation theorem #Abstract simplicial complex #Combinatorics #Complement (music) #h-vector #Projective plane #Simplicial manifold #Real projective plane #Projective test #Listing (finance) #Pure mathematics #Projective space #Simplicial set #Collineation #Geometry
- Cubic Partial Cubes from Simplicial Arrangements
2006/09/07 by David Eppstein · 2 citations
Engineering · Computer Science · Mathematics · #graph theory and CDMA systems #Advanced Graph Theory Research #Finite Group Theory Research #Mathematics #Combinatorics #Cube (algebra) #Simplicial complex #Construct (python library) #Plane (geometry) #Real projective plane #Projective plane #Projective test #Pure mathematics #Projective space #Geometry #Computer science #Complex projective space
- f-Vectors of Barycentric Subdivisions
2006/06/15 by Francesco Brenti, Brenti, Francesco, Volkmar Welker +1 · 4 citations
Computer Science · Mathematics · #05e99 #52c99 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Barycentric coordinate system #Combinatorics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Conjecture #Discrete mathematics #FOS: Mathematics #Geometry #Iterated function #Mathematical analysis #Mathematics #Polynomial #Polynomial and algebraic computation #Simplicial complex #Subdivision #math.AT #math.CO #msc:05e99 #msc:52c99
- Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps
2005/09/30 by Igor Belegradek · 1 citation
Computer Science · Mathematics · #3-manifold #Closed manifold #Combinatorics #Dimension (graph theory) #Fundamental group #Geometric and Algebraic Topology #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Invariant manifold #Manifold (fluid mechanics) #Mathematics #Physics #Polyhedron #Pure mathematics #Retract #Simplicial complex #Topological and Geometric Data Analysis #math.GR #math.GT #msc:20F65
- Model structures and the Oka Principle
2004/04/23 by Finnur Lárusson · 12 citations
Mathematics · #Abstract simplicial complex #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Covariance and contravariance of vectors #Functor #Holomorphic function #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Mathematics #Model category #Pure mathematics #Simplicial approximation theorem #Simplicial complex #Simplicial homology #Simplicial manifold #Simplicial set #Topology (electrical circuits) #h-vector
- Geometric Realization of Simplicial Complexes
1999/01/01 by Patrice Ossona de Mendez · 1 citation
Computer Science · Mathematics · #Abstract simplicial complex #Combinatorics #Computational Geometry and Mesh Generation #Computer science #Digital Image Processing Techniques #Dimension (graph theory) #Face (sociological concept) #Geometry #Grid #Mathematics #Order (exchange) #Partially ordered set #Pure mathematics #Realization (probability) #Simplicial approximation theorem #Simplicial complex #Simplicial homology #Simplicial manifold #Simplicial set #Sociology #Topological and Geometric Data Analysis
- Lattice points in lattice polytopes
1985/12/01 by U. Betke, P. McMullen, Peter McMullen · 5 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics #Commutative Algebra and Its Applications #Condensed matter physics #Hexagonal lattice #Integer lattice #Lattice (music) #Mathematics #Physics #Polytope #Simplicial complex
- Kneser's conjecture, chromatic number, and homotopy
1978/11/01 by László Lovász, L Lovász · 5 citations
Computer Science · Mathematics · #Advanced Topology and Set Theory #Chromatic scale #Combinatorics #Conjecture #Corollary #Discrete mathematics #Disjoint sets #Graph #Homotopy #Limits and Structures in Graph Theory #Mathematics #Pure mathematics #Simplicial complex #Topological and Geometric Data Analysis
- The Geometric Realization of a Semi-Simplicial Complex
1957/03/01 by John Milnor · 28 citations
Computer Science · Mathematics · #Abstract simplicial complex #Advanced Topics in Algebra #Algebra over a field #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Realization (probability) #Simplicial approximation theorem #Simplicial complex #Simplicial homology #Simplicial manifold #Simplicial set #Statistics #Topological and Geometric Data Analysis
- Semi-Simplicial Complexes and Singular Homology
1950/05/01 by Samuel Eilenberg, J. A. Zilber · 2 citations
Computer Science · Mathematics · #Algorithm #Amino acid #Biology #Combinatorics #Commutative Algebra and Its Applications #Genetics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Persistent homology #Pure mathematics #Simplicial complex #Simplicial homology #Topological and Geometric Data Analysis #h-vector