Sets with a negative number of elements
作者： D Loeb
DOI: 10.1016/0001-8708(92)90011-9
关键词: Combinatorics 、 Negative number 、 Mathematics 、 Discrete mathematics 、 Generalization 、 Multiset 、 Gaussian binomial coefficient 、 Symmetric function 、 Stirling number 、 Variable (mathematics) 、 Binomial coefficient
摘要: We will define an analog of a set which can contain either positive or negative number elements. allow sums to be calculated over arbitrary hybrid set. This lead us generalization symmetric functions variable agrees with all previous known generalizations in this direction. From these new functions, we calculate generalized binomial coefficients. Then coefficients given combinatorial interpretation terms partial order on the sets. Next, generalize linear partitions using and enumerate them. Finally, sum from one integer derive formulas involving them including Stirling numbers.
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