benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Suppose that k is a positive integer. A bijective map f:Z→Z is said to be k-[i]jumpy [/i] if |f(z)−z|≤k for all integers z. Is it that case that for every k, each k-jumpy map is a …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Suppose that kk is a positive integer. A bijective map f:Z→Zf : Z \to Z is said to be kk-[i]jumpy [/i] if |f(z)−z|≤k|f(z) - z| \le k for all integers zz. Is it that case that for every kk, each kk-jumpy map is a composition of 11-jumpy maps? [i]It is well known that this is the case when the support of the map is finite.[/i]
Plain-text mathematical notation (without MathML)
Suppose that k is a positive integer. A bijective map f:Z→Z is said to be k-[i]jumpy [/i] if |f(z)−z|≤k for all integers z.
Is it that case that for every k, each k-jumpy map is a composition of 1-jumpy maps?
[i]It is well known that this is the case when the support of the map is finite.[/i]
Original LaTeX notation
Suppose that $k$ is a positive integer. A bijective map $f : Z \to Z$ is said to be $k$-[i]jumpy [/i] if $|f(z) - z| \le k$ for all integers $z$.
Is it that case that for every $k$, each $k$-jumpy map is a composition of $1$-jumpy maps?
[i]It is well known that this is the case when the support of the map is finite.[/i]

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
79ee1d9a-8eb1-53f0-ba73-d0473169a336
task_key
test--79ee1d9a-8eb1-53f0-ba73-d0473169a336
task_revision_id
1
config / split
/ test

Official source

initial import