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Results tagged with co.combinatorics
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user 7458
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
votes
Is Cauchy induction used for proofs other than for AM–GM?
Another inequality can be proved by Cauchy induction :$$\prod_{i=1}^n(x_0+x_i)\geqslant\left(x_0+\prod_{i=1}^nx_i^{1/n}\right)^n\quad\text{for all}\quad n=1,2,...\;\text{and}\; x_0,...,x_n\geqslant0. …
- 2,437
24
votes
5
answers
3k
views
Is Cauchy induction used for proofs other than for AM–GM?
The proof by Cauchy induction of the arithmetic/geometric-mean inequality is well known. I am looking for a further theorem whose proof is much neater by this method than otherwise.
- 2,437