序列的单调分解
Decomposing sequences into monotonic subsequences
摘要：
称函数f：X -> Y是k-单调递增的，如果存在一个划分X = X_1U. U X_k使得f| X_i：X_i -> Y是单调递增的，其中i=1，.，K.证明了一对一函数f：N -> N是k-单调递增的当且仅当每一个k+1个正整数的集合包含两个整数x，x'且x < x'使得f（x）<= f（x '）.函数f：X \to Y称为k-单调的，如果存在一个划分X = X_1 U. U X_k使得f| X_i：X_i -> Y是单调递增或单调递减的，其中i=1，.，K.证明了不存在从N到Q的k-单调函数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
