1. Weighted Ehrhart functions
   2024/12/23 by Jesus A. De Loera, Enrique Reyes, Carlos E. Valencia +6 · 3 citations
   Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic number #Eulerian path #Generating function #Homogeneous #Lattice (music) #Polynomial #Polynomial and algebraic computation #Polytope #Semiring
2. Underlying Flag Polymatroids
   2022/07/25 by Alexander E. Black, Black, Alexander E., Raman Sanyal +1 · 1 citation
   Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Discrete mathematics #Enumeration #FOS: Mathematics #Flag (linear algebra) #Geometry #Mathematics #Matroid #Monotone polygon #Optimization and Control (math.OC) #Polytope #Pure mathematics #Simple (philosophy) #Subspace topology
3. Proving the solution of Malfatti’s marble problem
   2022/06/20 by G. Lombardi, Giancarlo Lombardi · 1 citation
   Arts and Humanities · Engineering · Mathematics · #Applied mathematics #Architecture and Art History Studies #Architecture and Computational Design #Calculus (dental) #Combinatorics #Convex body #Convex optimization #Engineering #Euclidean geometry #Extant taxon #Geometry #Mathematical economics #Mathematical optimization #Mathematics #Mathematics and Applications #Polytope #Regular polygon #Work (physics)
4. The Fuglede conjecture for convex domains is true in all dimensions
   2022/01/01 by Nir Lev, Máté Matolcsi · 17 citations
   Mathematics · #Analytic and geometric function theory #Combinatorics #Computer science #Conjecture #Convex optimization #Convex polytope #Convex set #Discrete mathematics #Geometry #Mathematical Analysis and Transform Methods #Mathematics #Omega #Physics #Point processes and geometric inequalities #Polytope #Regular polygon #Space (punctuation)
5. A friendly introduction to Fourier analysis on polytopes
   2021/04/12 by Sinai Robins, Robins, Sinai · 1 voice · 1 citation
   Computer Science · Mathematics · #Combinatorics #Computational Geometry and Mesh Generation #Divergence (linguistics) #Euclidean geometry #Euclidean space #Field (mathematics) #Fourier transform #Geometry #Mathematical analysis #Mathematics #Mathematics and Applications #Minkowski addition #Minkowski space #Point processes and geometric inequalities #Polytope #Polytope model #Pure mathematics #math.CO #math.NT
6. Characterizing and learning equivalence classes of causal DAGs under interventions
   2020/12/12 by L Solus, Liam Solus, Yuhao Wang +4 · 14 citations
   Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Algorithm #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Combinatorics #Computer science #Directed acyclic graph #Directed graph #Discrete mathematics #Genome Rearrangement Algorithms #Machine Learning and Algorithms #Mathematics #Permutation (music) #Polytope
7. The geometry of H 4 polytopes
   2020/07/01 by Tomme Denney, Da’Shay Hooker, De'janeke Johnson +3 · 1 citation
   Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Finite Group Theory Research #Coding theory and cryptography #Unimodular matrix #Polytope #Mathematics #Geometry #Section (typography) #Inscribed figure #Lattice (music) #Space (punctuation) #Combinatorics #Physics
8. Entropic Causality and Greedy Minimum Entropy Coupling
   2017/01/28 by Murat Kocaoglu, Kocaoglu, Murat, Alexandros G. Dimakis +5 · 3 citations
   Computer Science · Mathematics · #Applied mathematics #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Combinatorics #Entropy (arrow of time) #FOS: Computer and information sciences #Greedy algorithm #Information Theory (cs.IT) #Joint entropy #Joint probability distribution #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Mathematical optimization #Mathematics #Maximum entropy probability distribution #Polytope #Principle of maximum entropy #Random variable #Statistical Methods and Inference #Statistics #cs.AI #cs.IT #math.IT #stat.ML
9. The poset of rational cones
   2016/06/30 by Joseph Gubeladze, Mateusz Michałek · 1 citation
   Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithm #Combinatorics #Commutative Algebra and Its Applications #Cone (formal languages) #Conjecture #Homogenization (climate) #Mathematics #Order (exchange) #Partially ordered set #Polytope #Pure mathematics #Topological and Geometric Data Analysis #math.CO #math.NT #msc:20M13 #msc:52B20
10. Torus Decompostions of Regular Polytopes in 4-space
    2012/11/27 by Thomas F. Banchoff, Thomas Banchoff · 5 citations
    Computer Science · Mathematics · #Combinatorics #Computational Geometry and Mesh Generation #Computer science #Cube (algebra) #Geometry #Great circle #History and Theory of Mathematics #Inscribed figure #Mathematics #Mathematics and Applications #Octahedron #Perpendicular #Physics #Polyhedron #Polytope #Space (punctuation) #Stereographic projection #Symmetry (geometry) #Torus
11. Orientational Sampling Schemes Based on Four Dimensional Polytopes
    2010/07/07 by Salvatore Mamone, Giuseppe Pileio, Malcolm H. Levitt · 3 citations
    Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Mathematical Approximation and Integration #NMR spectroscopy and applications #Polytope #Computation #Sampling (signal processing) #Tensor (intrinsic definition) #Mathematics #Euler's formula #Spectral line #Combinatorics #Physics #Geometry #Mathematical analysis #Algorithm #Quantum mechanics
12. Geometry Revealed: A Jacob's Ladder to Modern Higher Geometry
    2010/01/01 by Marcel Berger, Lester J. Senechal · 1 citation
    Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics #Conic section #Convexity #Differential geometry #Geodesic #Geometric and Algebraic Topology #Geometry #History and Theory of Mathematics #Mathematics #Mathematics and Applications #Mathematics education #Physics #Plane (geometry) #Polyhedron #Polytope #Regular polygon #SPHERES #Surface (topology) #semigroups and automata theory
13. Lower bounds on the coefficients of Ehrhart polynomials
    2008/04/21 by Martin Henk, Makoto Tagami · 1 citation
    Agricultural and Biological Sciences · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Botanical Research and Chemistry #Combinatorics #Convex optimization #Convex polytope #Convex set #Counterexample #Discrete mathematics #Geometry #Lattice (music) #Mathematical analysis #Mathematics #Physics #Polytope #Regular polygon #Series (stratigraphy) #Upper and lower bounds
14. Semisymmetric graphs from polytopes
    2006/07/13 by Barry Monson, Tomaž Pisanski, Egon Schulte +1 · 1 citation
    Mathematics · Materials Science · #Finite Group Theory Research #Algebraic structures and combinatorial models #Nanocluster Synthesis and Applications #Mathematics #Combinatorics #Polytope #Symmetric graph #Transitive relation #Vertex (graph theory) #Graph #Toroid #Discrete mathematics #Line graph #Voltage graph
15. Moment polytopes for symplectic manifolds with monodromy
    2006/05/20 by San Vũ Ngọc · 6 citations
    Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Combinatorics #Geometric and Algebraic Topology #Geometry #Gravitational singularity #Hamiltonian (control theory) #Hamiltonian system #Integrable system #Mathematical analysis #Mathematics #Moment map #Monodromy #Nonlinear Waves and Solitons #Polytope #Pure mathematics #Regular polygon #Symplectic geometry
16. h^*-Vectors, Eulerian Polynomials and Stable Polytopes of Graphs
    2004/10/07 by Christos A. Athanasiadis · 1 citation
    Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Advanced Mathematical Identities #Polytope #Mathematics #Combinatorics #Lattice (music) #Order (exchange) #Dimension (graph theory) #Semigroup #Discrete mathematics
17. On approximability of linear ordering and related NP-optimization problems on graphs
    2003/09/16 by Sounaka Mishra, Kripasindhu Sikdar · 1 citation
    Computer Science · Mathematics · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Optimization and Search Problems #Combinatorics #Mathematics #Linear programming relaxation #Conjecture #Vertex (graph theory) #Polytope #Generalization #Maximum cut #APX #Approximation algorithm #Linear programming #Discrete mathematics #Mathematical optimization #Graph #Mathematical analysis
18. On the Complexity of Polytope Isomorphism Problems
    2003/06/01 by Volker Kaibel, Alexander Schwartz · 3 citations
    Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics #Complexity and Algorithms in Graphs #Convex set #Geometry #Graph #Graph Labeling and Dimension Problems #Induced subgraph isomorphism problem #Isomorphism (crystallography) #Mathematics #Polyhedral combinatorics #Polytope #Regular polygon
19. Abstract Regular Polytopes
    2002/12/12 by Peter McMullen, Egon Schulte · 2 citations
    Mathematics · #Mathematics and Applications #Polytope #Coxeter group #Polyhedron #Mathematics #Combinatorics #Polyhedral combinatorics #Discrete geometry #Group (periodic table) #Geometry and topology #Symmetry group #Geometry #Regular polygon #Physics
20. Multidimensional Ehrhart Reciprocity
    2002/01/01 by Matthias Beck · 2 citations
    Agricultural and Biological Sciences · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Botanical Research and Chemistry #Combinatorics #Corollary #Lattice (music) #Mathematics #Physics #Polytope #Pure mathematics #Reciprocity (cultural anthropology) #Reciprocity law #Simplex #Sociology
21. Helices and helix packings derived from the 3, 3, 5 polytope
    2001/08/01 by J.F. Sadoc, Jean‐François Sadoc · 2 citations
    Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · #Chemistry #Click Chemistry and Applications #Combinatorics #Crystallography #Folding (DSP implementation) #Geometry #Glycosylation and Glycoproteins Research #Helix (gastropod) #Homogeneous space #Mathematics #Polytope #Tetrahedron #Topology (electrical circuits) #Ubiquitin and proteasome pathways
22. The number of nets of the regular convex polytopes in dimension ⩽ 4
    1998/05/01 by Francis Buekenhout, F. Buekenhout, M. Parker +1 · 1 citation
    Computer Science · Mathematics · #Adjacency list #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Automorphism #Automorphism group #Cayley graph #Combinatorics #Convex analysis #Convex optimization #Convex polytope #Convex set #Dimension (graph theory) #Discrete mathematics #Facet (psychology) #Geometry #Graph #Graph theory and applications #Mathematics #Polytope #Regular polygon #Uniform k 21 polytope
23. The Order Dimension of Planar Maps
    1997/11/01 by Graham Brightwell, William T. Trotter · 1 citation
    Computer Science · Engineering · Mathematics · #Graph Labeling and Dimension Problems #graph theory and CDMA systems #Advanced Graph Theory Research #Combinatorics #Dimension (graph theory) #Mathematics #Polytope #Planar #Partially ordered set #Order (exchange) #Regular polygon #Convex polytope #Planar graph #Discrete mathematics #Convex set #Geometry #Computer science #Graph #Convex optimization
24. The Ehrhart Polynomial of a Lattice Polytope
    1997/05/01 by Ricardo Vázquez Díaz, Sinai Robins · 1 citation
    Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Mathematics #Polytope #Lattice (music) #Combinatorics
25. Almost optimal set covers in finite VC-dimension
    1995/12/01 by H. Brönnimann, Hervé Brönnimann, M. T. Goodrich +1 · 1 citation
    Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algorithm #Approximation algorithm #Binary logarithm #Combinatorics #Complexity and Algorithms in Graphs #Computational Geometry and Mesh Generation #Computational complexity theory #Computational geometry #Computer science #Constant (computer programming) #Cover (algebra) #Dimension (graph theory) #Discrete mathematics #Finite set #Geometry #Greedy algorithm #Mathematical analysis #Mathematics #Polytope #Set (abstract data type) #Set cover problem #Time complexity #Upper and lower bounds #VC dimension
26. Polytopes that fill ℝn and scissors congruenceand scissors congruence
    1995/06/01 by Jeffrey C. Lagarias, J. C. Lagarias, David Moews +1 · 1 citation
    Materials Science · Mathematics · #Combinatorics #Congruence (geometry) #Convex body #Convex hull #Convex polytope #Convex set #Cube (algebra) #Euclidean geometry #Geometric and Algebraic Topology #Geometry #Mathematical Dynamics and Fractals #Mathematics #Polytope #Quasicrystal Structures and Properties #Regular polygon
27. Realizations of regular apeirotopes
    1994/04/01 by Peter McMullen · 1 citation
    Engineering · Mathematics · #Algebra over a field #Combinatorics #Discrete mathematics #Euclidean geometry #Geometry #Mathematics #Mathematics and Applications #Point processes and geometric inequalities #Polytope #Pure mathematics #Realization (probability) #Symmetry (geometry) #graph theory and CDMA systems
28. The Order Dimension of Convex Polytopes
    1993/05/01 by Graham Brightwell, William T. Trotter · 3 citations
    Computer Science · Mathematics · Engineering · #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #graph theory and CDMA systems #Combinatorics #Polytope #Partially ordered set #Dimension (graph theory) #Mathematics #Convex polytope #Regular polygon #Order (exchange) #Convex set #Geometry #Convex optimization
29. A Monotonicity Property of h-vectors and h*-vectors
    1993/05/01 by Richard P. Stanley · 1 citation
    Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Class (philosophy) #Combinatorics #Commutative Algebra and Its Applications #Dimension (graph theory) #Discrete mathematics #Lattice (music) #Mathematical analysis #Mathematics #Monotonic function #Physics #Polytope
30. Portraits of a Family of Complex Polytopes
    1992/01/01 by H. S. M. Coxeter, G. C. Shephard · 1 citation
    Mathematics · Engineering · #Mathematics and Applications #History and Theory of Mathematics #graph theory and CDMA systems #Portrait #Polytope #Art #Computer science #Art history #Combinatorics #Mathematics

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