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Book: Polytopes

Binomial theorem


Federico Ardila

Lecture 1: Course is a combinatorial focus on convex polytopes and hyperplane arrangements.

Lecture 2: Definition of polytope P as convex hull of vertices. Sum of lambda x vertex where lambdas are nonnnegative and sum to 1.

Lecture 3: Intersections and products of polytopes are also polytopes.

Lecture 4: V-polyhedron intersected with affine plane is a V-polyhedron.

Lecture 5 and 6: Farkas' lemma versions 1 to 4.

Lecture 7: Faces of polytopes. Face of P in direction c is the set of all x in P where c-x is maximal.

Lecture 8: Construction of faces

Lecture 9: Face lattice

Lecture 10:

Lecture 11: The cyclic polytope.

Lecture 12: Graphs of polytopes

Lecture 13: How good is linear programming?

Lecture 14: Balinski's theorem: P is a d-polytope implies G(P) is d-connected.

Lecture 15: If P is simple, then G(P) determines P combinatorially.

Lecture 16: Complexes, subdivisions, triangulations.

Lecture 17: Triangulation of d-cross-polytope.

Lecture 18: Counting lattice points in polytopes.

Lecture 19: Partition functions.

Lecture 20: Generating functions for cones.

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Puslapis paskutinį kartą pakeistas 2019 vasario 03 d., 22:38