the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients...

mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed...

partition yields a partition of n − M into at most M parts. The Gaussian binomial coefficient is defined as: ( k + ℓ ℓ ) q = ( k + ℓ k ) q = ∏ j = 1 k + ℓ...

of p ( N , M , n ) {\displaystyle p(N,M,n)} is the following Gaussian binomial coefficient: ∑ n = 0 ∞ p ( N , M , n ) q n = ( N + M M ) q = ( 1 − q N +...

prime Factoriangular number Gamma distribution Gamma function Gaussian binomial coefficient Gould's sequence Hyperfactorial Hypergeometric distribution...

triangle Bernoulli's triangle Binomial expansion Cellular automata Euler triangle Floyd's triangle Gaussian binomial coefficient Hockey-stick identity Leibniz...

the binomial distribution, but for counts of multi-way occurrences (e.g., yes/no/maybe in a survey) Negative binomial distribution, for binomial-type...

lemma in relation to polynomials Gaussian binomial coefficient, also called Gaussian polynomial or Gaussian coefficient Gauss transformation, also called...

processing, one uses a discrete Gaussian kernel, which may be approximated by the Binomial coefficient or sampling a Gaussian. In geostatistics they have...

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is...

theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...

In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued...

the coefficient of x n {\displaystyle x^{n}} is found using binomial series to be ( n − 1 k − 1 ) {\displaystyle {\tbinom {n-1}{k-1}}} . Gaussian binomial...

algorithms such as Gaussian elimination and Cramer's rule to find solutions to the system. The leading entry (sometimes leading coefficient[citation needed])...

applying the Gaussian copula to credit derivatives to be one of the causes of the 2008 financial crisis; see David X. Li § CDOs and Gaussian copula. Despite...

processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would...

to define the q-binomial coefficients, also known as Gaussian coefficients, Gaussian polynomials, or Gaussian binomial coefficients: ( n k ) q = [ n...

q-factorials, one can move on to define the q-binomial coefficients, also known as the Gaussian binomial coefficients, as [ n k ] q = [ n ] ! q [ n − k ] ! q...

{n-1}{r-1}}_{q},} where the subscript q marks the notation for the Gaussian binomial coefficient, the number of subspaces of a given dimension within a vector...

dependent variable y {\displaystyle y} is a random variable that follows a Gaussian distribution, where the standard deviation is fixed and the mean is a linear...

Among the suggestions that have been given, the binomial kernels arising from the binomial coefficients stand out as a particularly useful and theoretically...

product-moment correlation coefficient (PPMCC), or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It is obtained by...

powerful insights into each or both of the sets. The symmetry of the binomial coefficients states that ( n k ) = ( n n − k ) . {\displaystyle {n \choose k}={n...

{q^{n+1-i}-1}{q^{i+1}-1}},} which is a Gaussian binomial coefficient, a q analogue of a binomial coefficient. Dimension 0 (no lines): The space is a...

Tanash, I.M.; Riihonen, T. (2020). "Coefficients for Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials [Data...

takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent...

algebraic dimension d in vector space V(n, q) is given by the Gaussian binomial coefficient, [ n d ] q = ( q n − 1 ) ( q n − q ) ⋯ ( q n − q d − 1 ) ( q...

coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coefficient to...

In mathematics, the Fibonomial coefficients or Fibonacci-binomial coefficients are defined as ( n k ) F = F n F n − 1 ⋯ F n − k + 1 F k F k − 1 ⋯ F 1...

Poisson distribution. The Poisson distribution is also the limit of a binomial distribution, for which the probability of success for each trial equals...