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Electronic Journal of Combinatorics
Article . 2012 . Peer-reviewed
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zbMATH Open
Article . 2012
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https://dx.doi.org/10.48550/ar...
Article . 2011
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DBLP
Article
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The Negative $q$-Binomial

The negative \(q\)-binomial
Authors: Shishuo Fu; Victor Reiner; Dennis Stanton; Nathaniel Thiem;

The Negative $q$-Binomial

Abstract

Interpretations for the $q$-binomial coefficient evaluated at $-q$ are discussed. A $(q,t)$-version is established, including an instance of a cyclic sieving phenomenon involving unitary spaces.

Country
Korea (Republic of)
Keywords

characteristic map, Combinatorial aspects of partitions of integers, cyclic sieving phenomenon, q-binomial, Representations of finite groups of Lie type, (q;t)-binomial, invariant theory, Combinatorial aspects of representation theory, unitary space, unitary group, ennola duality, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A10, 05A17, 05E10, 20C33, 51Exx, Factorials, binomial coefficients, combinatorial functions, Gaussian polynomial

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    popularity
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
gold