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Gaussian binomial coefficient

In mathematics, the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian numbers, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients. The Gaussian binomial coefficient, written as [ n k ] q {\displaystyle {\begin{bmatrix}n\\k\end{bmatrix}}_{q}} or ( n k ) q {\displaystyle {\binom…

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Quadratic Gauss sumSymmetric polynomialsPartitionsProjective spaceVector space
11 related topics

Q-identities

Pascal's identityLinear algebraBijectionBinomial theorem
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Definition

Empty productsRational function
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Combinatorial descriptions

InversionsCombinations
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Gaussian binomial coefficient

Nodes31
Edges30
Triples120
Avg. degree1.94
Density0.064516
Components1

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Gaussian binomial coefficient

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related to References · 87
Gaussian binomial coefficient → A29, Adv, Alexanderson, Amer, Andrews, Appl, Applications, Approx, Archived, Bernoulli, BF02075469, Bibcode, Binomial Coefficient, Binomial Coefficients, Boris, Borwein, Chichester, Cohn, Combinatorics, Construct
related to Counting subspaces over a finite field · 6
Gaussian binomial coefficient → For, Gaussian, Grassmannian, In, Schubert, When
related to Balls into bins · 4
Gaussian binomial coefficient → Applications, Indeed, Let, The Gaussian
related to Inversions · 4
Gaussian binomial coefficient → Gaussian, If, One, The
related to Analogs of Pascal's identity · 3
Gaussian binomial coefficient → Gaussian, Pascal's, The
related to Cyclic sieving phenomena · 3
Gaussian binomial coefficient → Gaussian, Let, The
related to Definition · 3
Gaussian binomial coefficient → For, If, The Gaussian
related to Reflection · 3
Gaussian binomial coefficient → Gaussian, In, Like
related to Symmetric polynomials and partitions · 3
Gaussian binomial coefficient → Equivalently, Gaussian, The
related to Gauss sums · 2
Gaussian binomial coefficient → Gauss, Gaussian

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binomial displaystyle coefficients gaussian coefficient doi mr number 10 also finite partitions polynomials q-binomial subspaces math space mathbb inversions polynomial

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SubjectPredicateObjectConfidenceSrc
Gaussian binomial coefficientrelated to Analogs of Pascal's identityThe0.60section
Gaussian binomial coefficientrelated to Analogs of Pascal's identityPascal's0.60section
Gaussian binomial coefficientrelated to Analogs of Pascal's identityGaussian0.60section
Gaussian binomial coefficientrelated to Balls into binsLet0.60section
Gaussian binomial coefficientrelated to Balls into binsThe Gaussian0.60section
Gaussian binomial coefficientrelated to Balls into binsIndeed0.60section
Gaussian binomial coefficientrelated to Balls into binsApplications0.60section
Gaussian binomial coefficientrelated to Counting subspaces over a finite fieldGaussian0.60section
Gaussian binomial coefficientrelated to Counting subspaces over a finite fieldIn0.60section
Gaussian binomial coefficientrelated to Counting subspaces over a finite fieldGrassmannian0.60section
Gaussian binomial coefficientrelated to Counting subspaces over a finite fieldWhen0.60section
Gaussian binomial coefficientrelated to Counting subspaces over a finite fieldSchubert0.60section

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