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Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.

11 votes
Accepted

Min–max reversing bijections $f:\mathbb{N}\to\mathbb{N}$

$\newcommand\N{\mathbb N}$No, it is not possible to have $\mu_{[\N]^2}\big({\operatorname{rev}(f)}\big) = 1$. Given the function $f$, we will say that $n\in\mathbb{N}$ is good if $f(n)<f(k)$ for more …
Saúl RM's user avatar
  • 10.6k
42 votes
2 answers
2k views

How decreasing can a bijection $f:\mathbb{N}\to\mathbb{N}$ be?

This is a follow-up to this question by Dominic van der Zypen. For each bijection $f:\mathbb{N}\to\mathbb{N}$, let $$\operatorname{rc}(f) := \liminf_{N\to\infty} \frac{\left|\left\{(m,n)\in\{1,\dots,N …
Saúl RM's user avatar
  • 10.6k