Decomposing sequences into monotonic subsequences
| dc.creator | Nathanson, Melvyn B. | |
| dc.creator | Parikh, Rohit | |
| dc.creator | Salame, Samer | |
| dc.date | 2006-03-27 | |
| dc.date.accessioned | 2026-07-07T07:07:16Z | |
| dc.date.available | 2026-07-07T07:07:16Z | |
| dc.description | The function f:X -> Y is called k-monotonically increasing if there is a partition X = X_1 U ... U X_k such that f|X_i : X_i -> Y is monotonically increasing for i=1,...,k. It is proved that a one-to-one function f:N -> N is k-monotonically increasing if and only if every set of k+1 positive integers contains two integers x,x' with x < x' such that f(x) <= f(x'). The function f:X \to Y is called k-monotonic if there is a partition X = X_1 U ... U X_k such that f|X_i : X_i -> Y is monotonically increasing or monotonically decreasing for i=1,...,k. It is also proved that there does not exist a k-monotonic function from N onto Q. | |
| dc.description | 4 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603634 | |
| dc.identifier | http://arxiv.org/abs/math/0603634 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110329 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | A60A6; 06A07 | |
| dc.title | Decomposing sequences into monotonic subsequences | |
| dc.type | text |