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Everything about Polyhedral combinatorics
Combinitorics of Polyhedra
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Polyhedral combinatoricsA 5-minute orientation
- Skim a recent paper: Synthesis of eugenol-functionalized polyhedral oligomer silsesquioxane for low-k bismaleimide resin combined with excellent mechanical and thermal properties as well as its composite reinforced by silicon fiberInfluential work since 2022
- Pick up a classic book: Geometry of Conditional IndependenceThe most-reprinted book on the subject
- Read the landmark paper: Polyhedral Combinatorics and Neural NetworksCited 56 times
- Go sideways: Convex polytopeA closely related topic
- Go sideways: Kalai's 3^d conjectureA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Polyhedral Combinatorics and Neural Networks
Multiple sequence alignment with arbitrary gap costs: Computing an optimal solution using polyhedral combinatorics
The Stochastic Shortest Path Problem: A polyhedral combinatorics perspective
Polyhedral geometry and combinatorics of an autocatalytic ecosystem
One-Bit-Matching Theorem for ICA, Convex-Concave Programming on Polyhedral Set, and Distribution Approximation for Combinatorics
Polyhedral combinatorics of UPGMA cones
Polyhedral Combinatorics and Network Reliability
Polyhedral combinatorics of multi-index axial transportation problems
🆕 Influential since 2022
Synthesis of eugenol-functionalized polyhedral oligomer silsesquioxane for low-k bismaleimide resin combined with excellent mechanical and thermal properties as well as its composite reinforced by silicon fiber
Polyhedral Au Nanoparticle/MoOx Heterojunction-Enhanced Ultrasensitive Dual-Mode Biosensor for miRNA Detection Combined with a Nonenzymatic Cascade DNA Amplification Circuit
Polyhedral combinatorics of bisectors
📚 Books worth reading
Geometry of Conditional IndependenceJason Ryder Morton · 2007
Integer points in polyhedraAlexander Barvinok · 2008
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean…
- Kalai's 3^d conjecture Unsolved problem in mathematics Does every d-dimensional centrally symmetric polytope have at least 3d nonempty faces? More unsolved problems in mathematics…
- Steinitz's theorem In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices…
- Polymake polymake is a software for the algorithmic treatment of convex polyhedra. Albeit primarily a tool to study the combinatorics and the geometry of convex…
- Gale diagram In the mathematical discipline of polyhedral combinatorics, the Gale transform turns the vertices of any convex polytope into a set of vectors or points…
- Hirsch conjecture In mathematical programming and polyhedral combinatorics, the Hirsch conjecture is the statement that the edge-vertex graph of an n-facet polytope in d-dimensio…
- Balinski's theorem In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional convex…
- Simplicial complex In mathematics, a simplicial complex is a structured set of simplices (for example, points, line segments, triangles, and their n-dimensional counterparts)…