Lesson plan
Alternating permutation
In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set {1, 2, 3, ..., n} is a permutation (arrangement) of those numbers so that each entry is alternately greater or less than the preceding entry. For example, the five alternating permutations of {1, 2, 3, 4} are: * 1, 3, 2, 4 because 1 2 2 1 1 1 n of alternating permutations of the set {1, ..., n} is called André's problem. The numbers A n are known as Euler numbers, zigzag numbers, or up/down numbers. When n is even the number A n is known as a secant number, while if n is odd it is known as a tangent number. These latter names come from the study of the generating function for the sequence.
Article summary
In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set {1, 2, 3, ..., n} is a permutation (arrangement) of those numbers so that each entry is alternately greater or less than the preceding entry. For example, the five alternating permutations of {1, 2, 3, 4} are: * 1, 3, 2, 4 because 1 2 2 1 1 1 n of alternating permutations of the set {1, ..., n} is called André's problem. The numbers A n are known as Euler numbers, zigzag numbers, or up/down numbers. When n is even the number A n is known as a secant number, while if n is odd it is known as a tangent number. These latter names come from the study of the generating function for the sequence.
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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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