用消极的思维获得结果
Getting results with negative thinking
摘要：
给定一个论域$U$，{ \em multiset}可以被认为是从$U$到自然数${\bf N}$的函数$M$。本文定义了一个{ \em混合集}为从论域$U$到整数${\bf Z}$的任意函数。这些集合被称为混合，因为它们包含具有正重数或负重数的元素。我们的目标是使用这些混合集{ \em好像}，他们是多集，以充分推广某些组合的事实，这是真正的经典只有非负整数。
英文摘要：
Given a universe of discourse $U$, a {\em multiset} can be thought of as a function $M$ from $U$ to the natural numbers ${\bf N}$. In this paper, we define a {\em hybrid set} to be any function from the universe $U$ to the integers ${\bf Z}$. These sets are called hybrid since they contain elements with either a positive or negative multiplicity. Our goal is to use these hybrid sets {\em as if} they were multisets in order to adequately generalize certain combinatorial facts which are true classically only for nonnegative integers.
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。
