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Getting results with negative thinking

S. Anelli·Ernesto Damiani·Ottavio D'Antona·Daniel E. Loeb
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Abstract

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.

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S. Anelli, Ernesto Damiani, Ottavio D'Antona, Daniel E. Loeb. 1995-02-09. Getting results with negative thinking. https://arxiv.org/abs/math/9502214

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