A problem of mine appeared in the lastest Mathematics Magazine:
Suppose $$\pi$$ is a permutation of $$\{1,2,\ldots,2m\}$$. Consider the (possibly empty) subsequence of $$\pi(m+1),\pi(m+2),\ldots,\pi(2m)$$ consisting of only those values which exceed $$\max\{\pi(1),\ldots,\pi(m)\}$$.

Let $$P(m)$$ denote the probability that this subsequence never decreases, when $$\pi$$ is a randomly chosen permutation of $$\{1,2,\ldots,2m\}$$. Evaluate the limit of $$P(m)$$ as $$m\to\infty$$.

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!