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Topic: Binomial coefficient

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Combinatorial proof

Fibonacci sequence

Catalan number

Recurrence relation

Coefficient

Laurent series

Euclidean plane

Addition

Poker probability

Fermi statistics

Taylor series

Quantum field theory

Sample space

Hyperbolic function

Pingala

	Binomial coefficient - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-06)
		This is generalized by the binomial theorem, which allows the exponent n to be negative or a non-integer.
		The binomial coefficients also occur in the formula for the binomial distribution in statistics and in the formula for a Bézier curve.
		This generalization is known as the generalized binomial coefficient and is used in the formulation of the binomial theorem and satisfies properties (3) and (7).
	encyclopedia.worldsearch.com /binomial_coefficient.htm (929 words)

	Binomial coefficient - Open Encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, in particular in combinatorics, the binomial coefficient of the natural number n and the integer k is defined to be the natural number
		The Catalan numbers have an easy formula involving binomial coefficients; they can be used to count various structures, such as trees and parenthesized expressions.
		This generalization is used in the formulation of the binomial theorem and satisfies properties (3) and (7).
	www.open-encyclopedia.com /Binomial_coefficient (867 words)

	Binomial coefficient (Site not responding. Last check: 2007-11-06)
		In mathematics in particular in combinatorics the binomial coefficient of the natural number n and the integer k is defined to be the natural
		Binomial coefficients are of importance in combinatorics because they provide ready formulas for frequent counting problems:
		The binomial coefficients also occur in the for the binomial distribution in statistics and in the formula for a Bézier curve.
	www.freeglossary.com /Binomial_coefficient (874 words)

	Binomial coefficient - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, particularly in combinatorics, the binomial coefficient of the natural number n and the integer k is defined to be the natural number
		is a polynomial in z of degree k with rational coefficients.
		The binomial coefficient has a q-analog generalization known as the Gaussian binomial.
	en.wikipedia.org /wiki/Binomial_coefficient (1234 words)

	Coefficient - Wikipedia, the free encyclopedia
		In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on.
		Important coefficients in mathematics include the binomial coefficients, coefficients in the statement of the binomial theorem, which can be partially found with Pascal's triangle.
		Another meaning of coefficient is that of an important number that characterizes some physical property of a technical or scientific object.
	en.wikipedia.org /wiki/Coefficient (180 words)

	Binomial - Wikipedia, the free encyclopedia
		In elementary algebra, a binomial is a polynomial with two terms: the sum of two monomials.
		The square of a binomial a + b is
		Pascal's triangle is not good to use with large numbers but as a rule of thumb will suffice where the power does not exceed 7.
	en.wikipedia.org /wiki/Binomial (242 words)

	Dorlands Medical Dictionary
		coefficient of inbreeding, an expression of the probability that an individual has received both alleles of a pair from a single ancestor common to both parents, or of the proportion of loci at which he is homozygous.
		The coefficient is calculated by dividing the concentration of the test compound at which it kills the test organism in 10 minutes, but not in 5 minutes, by the concentration of phenol that kills the organism under the same conditions.
		coefficient of thermal conductivity, a number indicating the quantity of heat that passes in a unit of time through a unit thickness of a substance when the difference in temperature is 1°C. coefficient of thermal expansion, the change in volume per unit volume of a substance produced by a 1°C temperature increase.
	www.mercksource.com /pp/us/cns/cns_hl_dorlands.jspzQzpgzEzzSzppdocszSzuszSzcommonzSzdorlandszSzdorlandzSzdmd_c_44zPzhtm (1991 words)

	Binomial theorem
		We found the binomial coefficients to be 1 5 10 10 5 1.
		Each coefficient is the previous coefficient multiplied by the exponent of a, and divided by the next exponent of b.
		That is, the row 1 2 1 are the coefficients of (a + b)².
	www.themathpage.com /aPreCalc/binomial-theorem.htm (951 words)

	The Binomial Distribution
		As a general rule, the binomial distribution should not be applied to observations from a simple random sample (SRS) unless the population size is at least 10 times larger than the sample size.
		The latter expression is known as the binomial coefficient, stated as "n choose k," or the number of possible ways to choose k "successes" from n observations.
		The binomial coefficient multiplies the probability of one of these possibilities (which is (1/2)²(1/2)² = 1/16 for a fair coin) by the number of ways the outcome may be achieved, for a total probability of 6/16.
	www.stat.yale.edu /Courses/1997-98/101/binom.htm (1250 words)

	Math Forum - Ask Dr. Math
		Usually, binomial expansion is introduced using a construction called Pascal's Triangle, but I prefer to think of it in terms of something called the binomial coefficient, which I'll explain later.
		Is it a coincidence that the (n)th row corresponds to the coefficients of the expansion (x+y)^n?
		In essence, the most common use of binomial expansion is in expression simplification; the expansion is usually done when you expect terms to cancel.
	mathforum.org /library/drmath/view/56381.html (900 words)

	Binomial coefficient (Site not responding. Last check: 2007-11-06)
		In mathematics, in particular in combinatorics, the binomial coefficient of the natural number n and the integer k is definedto be the natural number
		Binomial coefficients are of importance in combinatorics, because theyprovide ready formulas for certain frequent counting problems:
		The binomial coefficients also occur in the formula for the binomial distribution in statistics and in theformula for a Bézier curve.
	www.therfcc.org /binomial-coefficient-74425.html (686 words)

	Binomial Trees, Forests, and Heaps
		If we have labels (keys) on the nodes of a binomial tree, and we impose an ordering property where the parent key is larger than the keys of any of its children, we can construct a heap with a binomial queue.
		Binomial heaps are important because of the efficient way in which two heaps can be merged.
		For example, this same scheme could be used with the binomial heap where the items in the BST store a pointer to the node in the binary tree representation of the heap, rather than indices in the heap array.
	www.cs.rutgers.edu /~kaplan/503/handouts/binomialQ.html (1682 words)

	Short course on asymptotics
		The largest of the binomial coefficients (n choose k) is the middle one, with k = [n/2].
		The sum of the binomial coefficients (n choose k) over all k from 0 to n is 2^n, by the binomial theorem.
		A well-known relation for binomial coefficients states that the sum over the squares of the coefficients (n choose k), from k=0 to k=n, is equal to the coefficient (2n choose n).
	www.math.uiuc.edu /~hildebr/reu02/asymptotics.html (1019 words)

	binomial_coefficient (Site not responding. Last check: 2007-11-06)
		denotes the factorial of ''m''.) The binomial coefficient of ''n'' and ''k'' is also written as C(''n'', ''k'') or C
		The '''binomial coefficient''' of the integer numbers ''n'' and ''k'' is defined as a coefficient of the
		Binomial coefficient is a partial case of multinomial coefficient.
	q-basic.xodox.de /binomial_coefficient (941 words)

	Combination article - Combination combinatorics k-subsets binomial coefficient permutations factorial - What-Means.com (Site not responding. Last check: 2007-11-06)
		Combinations are studied in combinatorics: let S be a set; the combinations of this set are its subsets.
		The number of k-combinations or k-subsets of set with n elements is the binomial coefficient "n choose k", written as
		It is useful to note that C(n, k) can also be found using Pascal's triangle, as explained in the binomial coefficient article.
	www.what-means.com /encyclopedia/Choose (188 words)

	PlanetMath: upper and lower bounds to binomial coefficient
		"upper and lower bounds to binomial coefficient" is owned by rspuzio.
		proof of upper and lower bounds to binomial coefficient
		This is version 3 of upper and lower bounds to binomial coefficient, born on 2003-03-04, modified 2004-11-20.
	www.planetmath.org /encyclopedia/UpperAndLowerBoundsToBinomialCoefficient.html (81 words)

	Binomial Distribution (Site not responding. Last check: 2007-11-06)
		In mathematics, the binomial distribution is a discrete probability distribution which describes the number of successes in a sequence of n independent yes/no experiments, each of which yielding success with probability p.
		The number of HIV-positives you pick is a random variable X which follows a binomial distribution with n = 500 and p =.05.
		is the binomial coefficient "n choose k" (also denoted C(n, k)), whence the name of the distribution.
	www.wikiverse.org /binomial-distribution (595 words)

	[No title]
		The Catalan numbers have an easy formula involving binomial coefficients; they can be used to count various structures, such as
		The binomial coefficients also occur in the formula for the
		binomial distribution in statistics and in the formula for a Bézier curve.
	en-cyclopedia.com /wiki/Binomial_coefficient (681 words)

	SDL Delphi Component Suite - BinomCoeff (Site not responding. Last check: 2007-11-06)
		The function BinomCoeff calculates the binomial coefficient (n,k), which is the number of possible combinations when drawing k items out of a total set of n.
		Please note that the binomial coefficient may become too large to be returned as longint value.
		If you expect large binomial coefficients you maybe want to use the function LnBinomCoeff, which calculates the natural logarithm of it.
	www.lohninger.com /helpcsuite/binomcoeff.htm (104 words)

	Binomial Probabilities (Site not responding. Last check: 2007-11-06)
		Identify a trial, a success, the values for p and n, and the possible values of X. Probabilities associated with a binomial experiment having a large sample space are typically calculated using the binomial probability formula.
		The purpose of this exploration is to use the binomial probability formula to calculate probabilities.
		Calculate the binomial coefficient C(3, 0), C(3, 1), C(3, 2) and C(3, 3) by using the binomial coefficient formula.
	faculty.frostburg.edu /math/monline/stat/43_p1.html (1561 words)

	PlanetMath: central binomial coefficient
		th central binomial coefficient is defined to be
		Note that the set of these numbers meeting this alternate criterion is a superset of those meeting the first criterion, since for
		This is version 2 of central binomial coefficient, born on 2004-06-21, modified 2004-06-21.
	planetmath.org /encyclopedia/CentralBinomialCoefficient.html (90 words)

	PlanetMath: binomial coefficient
		Properties 5 and 6 are the binomial theorem applied to
		Although the standard mathematical notation for the binomial coefficients is
		This is version 24 of binomial coefficient, born on 2001-10-17, modified 2005-07-27.
	planetmath.org /encyclopedia/BinomialCoefficient.html (208 words)

	SurfStat.australia (Site not responding. Last check: 2007-11-06)
		The distribution of the count of successes is called the binomial distribution with two parameters, n and p, required to determine P(X=x).
		Then X has binomial distribution with n=3 and p=0.5, outcome win(W) or Lose(L) on each trial.
		Binomial distributions are used to model situations which can be thought of as repeated independent "trials" each with only 2 possible outcomes.
	www.anu.edu.au /nceph/surfstat/surfstat-home/3-2-3.html (360 words)

	Arithmetic (Scalable Simulation Framework)
		Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
		If coefficients are for the interval a to b, x must have been transformed to x -> 2(2x - b - a)/(b-a) before entering the routine.
		If the coefficients are for the inverted interval, in which (a, b) is mapped to (1/b, 1/a), the transformation required is x -> 2(2ab/x - b - a)/(b-a).
	www.ssfnet.org /javadoc/cern/jet/math/Arithmetic.html (380 words)

	Pascal Triangle
		The famous French mathematician Pascal suggested a very simple way of the binomial coefficients calculation by means of their disposition in the form of certain array called the arithmetical square or Pascal triangle.
		Each binomial coefficient inside Pascal triangle are calculated according to (3).
		The binomial coefficients and the Pascal triangle are widely practiced in different branches of mathematics.
	www.goldenmuseum.com /0901Triangle_engl.html (581 words)

	Binomial (Site not responding. Last check: 2007-11-06)
		In elementary algebra a binomial is a polynomial with two terms: the sum of monomials.
		It is the simplest kind of In biology Binomial nomenclature is a naming convention for all things.
		See also: completing the square binomial distribution binomial coefficient.
	www.freeglossary.com /Binomial (408 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		We know that Lucas' theorem says that the binomial coefficient (nCk) is odd iff no 0 appears above a 1 when you write the binary representation of n above the binary representation of k.
		Is there is a natural definition of a "2-adic binomial coefficient", B, so that for any 2-adics integers n,k, nBk is a 2-adic integer which is odd iff the generalized Lucas condition holds?
		By "natural" I mean that nBk=nCk when k is a nonnegative integer and that many of the usual binomial coefficient identities still hold.
	www.lehigh.edu /~dmd1/km61.txt (185 words)

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