Lesson plan
Hypersimplex
In polyhedral combinatorics, the hypersimplex \Delta_{d,k} is a convex polytope that generalizes the simplex. It is determined by two integers d and k , and is defined as the convex hull of the d -dimensional vectors whose coefficients consist of k ones and d-k zeros. Equivalently, \Delta_{d,k} can be obtained by slicing the d -dimensional unit hypercube [0,1]^d with the hyperplane of equation x_1+\cdots+x_d=k and, for this reason, it is a (d-1) -dimensional polytope when 0 .
Article summary
In polyhedral combinatorics, the hypersimplex \Delta_{d,k} is a convex polytope that generalizes the simplex. It is determined by two integers d and k , and is defined as the convex hull of the d -dimensional vectors whose coefficients consist of k ones and d-k zeros. Equivalently, \Delta_{d,k} can be obtained by slicing the d -dimensional unit hypercube [0,1]^d with the hyperplane of equation x_1+\cdots+x_d=k and, for this reason, it is a (d-1) -dimensional polytope when 0 .
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.