binomial coefficient


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Related to binomial coefficient: binomial theorem, binomial distribution

binomial coefficient

[bī′nō·mē·əl kō·ə′fish·ənt]
(mathematics)
A coefficient in the expansion of (x + y) n , where n is a positive integer; the (k + 1)st coefficient is equal to the number of ways of choosing k objects out of n without regard for order. Symbolized (nk); nCk ; C (n,k); Cnk.
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Focusing first on the results presented in column (a), we see that the estimated negative binomial coefficients for the terms which interact the cultural distance variable and the dummy variables that identify the immigrants' skill levels are all negative and significantly different from zero.
Considering the results presented in column (b), we see the sum of the negative binomial coefficients on the term which interacts the low-skilled cohort dummy variable with the cultural distance variable and the term which interacts the low-skilled cohort dummy variable with the cultural distance variable and the lagged immigrant stock variable is significantly different from the corresponding summations for the medium- (p = 0.
Source-destination cultural differences, immigrants' skill levels, and immigrant stocks: evidence from six OECD member countries
Let C(t) and CB(t) denote the generating functions for the Catalan numbers and the central binomial coefficients, that is,
Number of cycles in the graph of 312-avoiding permutations
In this section we present some basic notions on words and binomial coefficients of words.
9, page 93) the infiltration product in an algebraic framework; Ochsenschlager (see [12]) defined this product independently in the context of binomial coefficients of words (see the next section).
Hopf algebra of permutation pattern functions (extended abstract)
The eigenvalues of a right-circulant matrix with binomial coefficients are given by
The formula for the n-th term of the right-circulant determinant sequence with binomial coefficients, denoted by [R.
Circulant determinant sequences with binomial coefficients
Some further results on reciprocals of the central binomial coefficients have recently also been obtained by Sprugnoli (6).
In this section we develop integral identities for products of reciprocals of binomial coefficients.
Some properties of reciprocals of double binomial coefficients
kxn], we obtain the following corollary that will be a key step in connecting the poset binomial coefficients to supercharacters.
Rainbow supercharacters and a poset analogue to q-binomial coefficients
Since the coefficients of these polynomials can be expressed in terms of binomial coefficients, Boros and Moll also made the statement:
Prove that the binomial coefficients are [infinity]-logconcave.
Infinite log-concavity: developments and conjectures

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