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Generalized Binomial Coefficients and the Subset–Subspace Problem

✍ Scribed by John Konvalina

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
150 KB
Volume
21
Category
Article
ISSN
0196-8858

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✦ Synopsis

Generalized binomial coefficients of the first and second kind are defined in terms of object selection with and without repetition from weighted boxes. The combinatorial definition unifies the binomial coefficients, the Gaussian coefficients, and the Stirling numbers and their recurrence relations under a common interpretation. Combinatorial proofs for some Gaussian coefficient identities are derived and shown to reduce to the ordinary binomial coefficients when q s 1. This approach provides a different perspective on the subset᎐subspace analogy problem. Generating function relations for the generalized binomial coefficients are derived by formal methods.

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