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Getting results with negative thinking

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Publication:6502421

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arXivmath/9502214MaRDI QIDQ6502421

Author name not available (Why is that?)

Abstract: Given a universe of discourse

U

, a {em multiset} can be thought of as a function

M

from

U

to the natural numbers

. In this paper, we define a {em hybrid set} to be any function from the universe

U

to the integers

. 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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