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Topic: Stirling number

Related Topics

Bell numbers

Factorial

Integer partition

Partition of a set

Limit (mathematics)

James Stirling

James Stirling (mathematician)

Bose Einstein statistics

Normal distribution

Probability density function

Pi

Integral

Ivo Lah

Calculus

Boltzmann factor

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	What's Special About This Number?
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	www.stetson.edu /~efriedma/numbers.html (7292 words)

	What's special about this number? (5)
		is a triangular number: 1 + 2 + 3 + … + 19 + 20 + 21
		is the number of 7 by 7 symmetric permutation matrices.
		is a deficient number, and the number of planar partitions of 12.
	www.archimedes-lab.org /numbers/Num201_500.html (2483 words)

	Интересные числа 2
		is the number of planar partitions of 17.
		is the number of planar partitions of 18.
		is the number of planar partitions of 19.
	arbuz.uz /z_numbers2.html (3655 words)

	GNU Emacs Calc 2.02 Manual
		If the number is a non-integral real number, the generalized factorial is used, as defined by the Euler Gamma function.
		Each step either discovers that the number is non-prime, or substantially increases the certainty that the number is prime.
		commands to increase your certainty that the number is indeed prime.
	www.delorie.com /gnu/docs/calc/calc_220.html (832 words)

	PlanetMath: Stirling numbers of the first kind
		This generating function implies a number of identities.
		Q.E.D. "Stirling numbers of the first kind" is owned by rmilson.
		This is version 3 of Stirling numbers of the first kind, born on 2002-03-31, modified 2004-11-01.
	planetmath.org /encyclopedia/StirlingNumbersOfTheFirstKind.html (368 words)

	PlanetMath: Stirling numbers of the second kind
		Indeed, the Stirling numbers of the second kind can be characterized as the coefficients involved in the corresponding change of basis matrix, i.e.
		Q.E.D. "Stirling numbers of the second kind" is owned by rmilson.
		This is version 8 of Stirling numbers of the second kind, born on 2002-03-29, modified 2007-03-28.
	planetmath.org /encyclopedia/StirlingNumbersSecondKind.html (504 words)

	Stirling Triathlon Club > Home
		Stirling Triathlon Club also collects anonymous demographic information, which is not unique to you, such as your ZIP code, age, gender, preferences, interests and favorites.
		Stirling Triathlon Club may also contact you via surveys to conduct research about your opinion of current services or of potential new services that may be offered.
		Stirling Triathlon Club may, from time to time, contact you on behalf of external business partners about a particular offering that may be of interest to you.
	www.stirlingtri.co.uk /Home/tabid/36/ctl/Privacy/Default.aspx (970 words)

	Clan Stirling Online! Research Library Article
		Stirling is the most strategically important of all the castles in Scotland.
		The town of Stirling is situated on the eastern declivity of a hill, terminating, to the west, in a perpendicular basaltic rock, on the summit of which is the Castle.
		In 1566 Stirling was once again chosen as the refuge of a royal infant when the two month old Prince James, son of Mary (later James VI) was moved there by feuding Scottish lords.
	www.clanstirling.org /Main/lib/castle/StirlingCastle-1830s.html (656 words)

	Stirling number
		In combinatorics, Stirling numbers of the second kind S(n,k) (with a capital "S") count the number of equivalence relations having k equivalence classes defined on a set with n elements.
		In particular, the nth moment of the Poisson distribution with expected value 1 is precisely the number of partitions of a set of size n, i.e., it is the nth Bell number (this fact is "Dobinski's formula").
		Unsigned Stirling numbers of the first kind s(n,k) (with a lower-case "s") count the number of permutations of n elements with k disjoint cycles[?].
	www.ebroadcast.com.au /lookup/encyclopedia/st/Stirling_number.html (114 words)

	Stirling Number - LocalArtGallery.com (Site not responding. Last check: )
		Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second kind.
		Stirling numbers of the first kind are written with a small s, and those of the second kind with a large S (Abramowitz and Stegun use an uppercase S and a flletter S respectively).
		Stirling numbers of the second kind S(n,k) (with a capital "S") count the number of the number of ways to partition a set of n elements into k nonempty subsets.
	www.localartgallery.com /encyclopedia/Stirling_number (726 words)

	Opperman Stirling
		The Stirling was unsuccessful, not due to any fault with the car, but because the company did not have the credibility and influence of more established car makers.
		Stirling number 1 had a version of the Excelsior twin-cylinder two-stroke engine enlarged from the usual 328cc to 424cc, and fitted at the front.
		The pictures here show Stirling number 2, which incorporated various modifications, the most important of which was the use of an Austrian Steyr-Puch twin-cylinder four-stroke of half-a-litre, at the rear.
	www.rumcars.org /c-opperman.html (201 words)

	Stirling number
		In combinatorics, unsigned Stirling numbers of the first kind :''s''(''n'',''k'') (with a lower-case "''s''") count the number of permutations of n elements with k disjoint cycles.
		Stirling numbers of the first kind (without the qualifying adjective unsigned) are the coefficients in the expansion :
		Stirling numbers of the first kind can be expressed in terms of the harmonic numbers as follows: :
	www.keywordmage.net /st/stirling-number.html (254 words)

	Bambooweb: Stirling number
		Stirling numbers of the first kind (without the qualifying adjective unsigned) are the coefficients in the expansion
		Stirling numbers of the second kind S(n,k) (with a capital "S") count the number of equivalence relations having k equivalence classes defined on a set with n elements.
		In recent years, the Stirling numbers of the second kind have often been denoted in a way introduced by Donald Knuth:
	www.bambooweb.com /articles/s/t/Stirling_number.html (164 words)

	Stirling numbers@Everything2.com
		stirling numbers of the second kind are used to determine how many ways an n-set can be partitioned into m non-empty subsets.
		these numbers are also sometimes represented in a triangle, since half the chart is empty where m > n, that is, where the number of partitions is 0.
		The number of possible partitionings which put n in its own set is equal to the number of partitionings of a set of cardinality n-1 into m-1 non-empty subsets, which is precisely the value S(n-1,m-1).
	www.everything2.com /index.pl?node_id=794897 (408 words)

	Majestic Group Investments Closed-Ended Funds
		Stirling Mortimer Global Property Fund PCC Limited is a registered closed-ended Guernsey domiciled protected cell company with limited liability.
		A key and differentiating feature of the Stirling Mortimer funds is that they seek to provide attractive returns from property investment over a comparatively short period of time; approximately two years.
		It is Stirling Mortimers intention where possible to only release Investment Funds to the markets that offer investors an element of capital protection and the opportunity of a reasonable return.
	www.majesticinvestments.com /en/closed_ended_funds.php (439 words)

	From the Geometric Series to Stirling Numbers
		Stirling was a follower of Newton, and elaborated Newton's scheme for classifying the cubics.
		Later, Stirling became manager of the Scottish Mining Company, a demanding job which made it difficult for him to continue with the study of mathematics and physics.
		The left-most column of the coefficient matrix is a row of the Eulerian numbers, the two right-most columns of the coefficient matrix are rows of the binomial coefficients, and the right-hand column vector is a row of Stirling numbers (of the first kind).
	www.mathpages.com /home/kmath529/kmath529.htm (817 words)

	Stirling number - OneLook Dictionary Search
		We found one dictionary with English definitions that includes the word Stirling number:
		Tip: Click on the first link on a line below to go directly to a page where "Stirling number" is defined.
		Phrases that include Stirling number: stirling number of the first kind
	www.onelook.com /?w=Stirling+number&ls=a (82 words)

	Stirling's Triangles - Wolfram Demonstration Project
		Displays Stirling numbers of the first and second kind for up to ten columns.
		Stirling numbers of the first kind satisfy the recurrence
		Stirling Number of the Second Kind (Wolfram MathWorld)
	demonstrations.wolfram.com /StirlingsTriangles (123 words)

	Stirling Council: Business » Trading Standards » Scams
		There are also a number of organisations that offer to purchase foreign lottery tickets on a consumer's behalf, or offer entry into lottery syndicates.
		The matrix works by sending the person at the top of the list their 'free gift' only after a prescribed number of new recruits has signed up – the prescribed number varies according to the choice of 'free gift' but can be as great as 100.
		The adverts, which have a freephone number to call, are usually placed in the classified sections of free or local newspapers.
	www.stirling.gov.uk /index/business/tradingstandards/ts-scams.htm (3598 words)

	Business valuation UK - Stirling Business Solutions, a business transfer and valuation company
		Obviously, there are a number of other reasons why you might want to carry out a valuation of a business; it might be that someone is considering selling part or all of it, or that someone is interested in purchasing it.
		It might be on the death of an owner, or for drawing up a will, or it might just be because the owner wants to know what he or she is worth.
		To add to the complications, there are a number of different methods of conducting a valuation of a business.
	www.stirling-uk.com /valuations.html (826 words)

	Numerical Modeling of Cryocoolers (Cryogenics Refrigerators, Coolers, Engines)
		The equations of the conservation of energy (both gas and wall), conservation of mass and momentum are solved at each node until the solution converges.
		Figure 1 is a schematic diagram of a dual-compressor Stirling cooler.
		The optimum frequency predicted by the model compares favorably with the experimentally determined optimum frequency of the cooler.
	www.yutopian.com /Yuan/MCooler.html (1064 words)

	Dictionary of Combinatorics -- S
		There need not be an identity element (as there must be in a monoid), nor is there a requirement that every element must have an inverse (as there is in a group), indeed, without an identity the existance of inverses becomes impossible to define.
		The Stirling numbers of the second kind, S(n,t), have the combinatorial interpretation of counting the number of ways of partitioning an n element set into t non-empty subsets.
		The Stirling numbers of the first kind, s(n,t), are the coefficients on the monomials in an expansion of polynomials of the form
	www.southernct.edu /~fields/comb_dic/S.html (533 words)

	Stirling number - Article from FactBug.org - the fast Wikipedia mirror site (Site not responding. Last check: )
		Stirling numbers of the first kind are sometimes written with the alternate notation
		Stirling numbers of the first kind can be expressed in terms of the harmonic numbers as follows:
		In recent years, the Stirling numbers have often been denoted in a way introduced in 1935 by Jovan Karamata and promoted later by Donald Knuth:
	www.factbug.org /cgi-bin/a.cgi?a=95465 (286 words)

	Lah number . 1955 . Ivo Lah . Stirling number (Site not responding. Last check: )
		In mathematics, Lah numbers, discovered by Ivo Lah in 1955 are coefficients expressing rising factorials in terms of falling factorials.
		Unsigned Lah numbers have an interesting meaning in combinatorics: they count the number of ways a set of n elements can be partitioned into k nonempty subsets that are linearly ordered.
		In recent years, the Stirling numbers have often been denoted in a way introduced in 1935 by Jovan...
	www.uk.fraquisanto.net /Lah_number (395 words)

	Stirling Number of the First Kind - Science Forums
		For the uninitiated, s[n,k] is a Stirling number of the first kind and represents (as I was explained) the number of ways of sitting n people in k table so that every table has at least one person.
		Suppose each of the n persons is wearing a t-shirt with a number on it between 1 and n where no two persons have the same number.
		For number 4, you have 4 choices to sit to the left of A, and 3 choices to sit to the right of A. Everyone else's seat would then not matter.
	www.scienceforums.net /forum/showthread.php?p=78022 (1930 words)

	Stirling Denmark - Biomass Based Energy
		The company - STIRLING DENMARK - is a spin-out from the Technical University of Denmark, founded on April 29, 2004 to commercialise 15 years of focussed research and development within Stirling engine technology, conducted by Professor Henrik Carlsen.
		The future commercialisation was always one of the design considerations, and hence, the Stirling engines are designed for volume production and for many years of smooth operation, based on regular service intervals.
		As a result of this effort, Henrik Carlsen is today recognized as one of the world leading experts and academics within applied Stirling engine technologies and his engine designs have demonstrated continuous operation on biofuels, where all other attempts to provide stable solutions so far have failed.
	www.stirling.dk /default.asp?ID=120 (238 words)

	Paramount Stirling Highland Hotel in Stirling, United Kingdom
		Built in 1854 as the High School of Stirling, it is close to Stirling Castle and all the attractions of the City.
		Dating back to 1854, the former high school of Stirling has retained many of the original school house features including the fully working observatory at the top of the building, and memorabilia from former pupils.
		Located in the centre of Stirling, just a stroll from the town's famous landmark Castle, this wonderful hotel has recently been upgraded with refurbished bedrooms, offering first class accommodation, fine dining and a traditional warm Scottish welcome.
	www.world-stay.com /en/dist1/117858/Paramount-Stirling-Highland-Hotel-Stirling.html (496 words)

	Stirling's Triangle for Subsets
		The number of ways of partitioning a set of n elements into m non-empty sets (i.e., m blocks), also called a Stirling set number.
		Stirling numbers of the second kind obey the recurrence relations
		``Stirling Numbers of the Second Kind.'' §24.1.4 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
	steiner.math.nthu.edu.tw /chuan/123/test/stirling-subsets.htm (199 words)

	Logarithm of Stirling numbers of the second kind
		Hello, I have a problem in which I need to calculate the logarithm of Stirling numbers of the second kind for large n (in the range 1 to thousands and preferably millions) and m in the same range.
		Due to the large range for n and m I prefer not to work with the Stirling numbers of the second kind directly, as my working precision is not that great.
		An approximation with errors (of the natural logarithm of the Stirling number of the second kind) up to +-10 would still be useful for me, although the more accurate the better of course.
	www.usenet.com /newsgroups/sci.math/msg18935.html (172 words)

	Information on Set Partitions
		The number of partitions of an n-set into k blocks is called a Stirling number of the second kind and is denoted S(n,k).
		Sometimes ther Stirling numbers of the second kind are written in a manner similar to the binomial coefficients, except that curly braces are used instead of parentheses.
		Information about James Stirling, for whom the Stirling numbers of the second kind are named.
	www.theory.csc.uvic.ca /~cos/inf/setp/SetPartitions.html (544 words)

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