Număr Erdős
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Prin număr Erdős (API: /ɛrdøːʃ/), conferit în onoarea matematicianului ungar Paul Erdős (1913 - 1996), considerat unul dintre cei mai prolifici autori de articole de matematică din toate timpurile, se înţelege un mod de a descrie "distanţa de colaborare" relativă, referitoare la scrierea de articole matematice dintre un anumit autor de astfel de lucrări şi Erdős.
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[modifică] Definiţie
In order to be assigned an Erdős number, an author must co-write a mathematical paper with an author with a finite Erdős number. Paul Erdős is the one person having an Erdős number of zero. If the lowest Erdős number of a coauthor is k, then the author's Erdős number is k+1.
Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators[1]; these are the people with Erdős number 1. The people who have collaborated with them (but not with Erdős himself) have an Erdős number of 2 (8,162 people as of 2007), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has no Erdős number (or an undefined one).
There is room for ambiguity over what constitutes a link between two authors; the Erdős Number Project website says "Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional co-authors is permitted," but they do not include non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The “Erdős number of the second kind” restricts assignment of Erdős numbers to papers with only two collaborators.[2]
The Erdős number was most likely first defined by Casper Goffman, an analyst whose own Erdős number is 1.[3] Goffman published his observations about Erdős's prolific collaboration in a 1969 article entitled "And what is your Erdős number?"[4]
The AMS collaboration distance calculator allows an online calculation of an individual's Erdős number.
[modifică] Impact
[modifică] Efectul decesului lui Erdős asupra numărului Erdős
Given that Erdős died in 1996 and no works of his remain to be published, it is no longer possible for a person to be newly assigned an Erdős number of 1. Likewise, once everyone with an Erdős number of 1 has died and have no work remaining to be published, it will be impossible for a new person to obtain an Erdős number of 2, and so on.
[modifică] În afara matematicii
[modifică] Număr Bacon
[modifică] Număr Kibo
[modifică] Număr Stringfield
Similar, numărul Stringfield este o aplicare a aceleiaşi idei în domeniul ufologie, cercetarea obiectelor zburătoare neindentificate, conectând într-o reţea socială pe cei care au co-investigat sau co-studiat fenomenele UFO împreună cu Leonard H. Stringfield, din anii săi târzii.
[modifică] Anectodica numărului Erdős
Se spune în glumă că faimosul jucător american de baseball Hank Aaron ar avea un număr Erdős 1 pentru că atât el cât şi Erdős au semnat pe aceeaşi minge de basebal în ziua când Emory University i-a premiat simultan pe ambii cu un doctorat onorific.
Conform datelor din iunie 2007, departamentul de matematică al University of Memphis, Tennessee avea cei mai mulţi angajaţi cu un număr Erdős 1 dintre toate departamentele de matematică al oricărei universităţi din lume. În ordine alfabetică, aceşti matematicieni sunt Béla Bollobás, Ralph Faudree, Jeno Lehel, Cecil C. Rousseau şi Richard Schelp. Trei dintre aceştia sunt printre primii zece, cei mai frecvenţi colaboratori direcţi ai lui Erdős. [3][4]
[modifică] Vezi şi
[modifică] Referinţe
- ^ Erdős Number Project
- ^ Grossman et al. “Erdös numbers of the second kind,” in Facts about Erdös Numbers and the Collaboration Graph. Erdös Number Project, [1], retrieved January 9, 2008.
- ^ [2] Michael Golomb's obituary of Paul Erdős
- ^ Goffman, Casper (1969). „And what is your Erdős number?”. American Mathematical Monthly 76.
[modifică] Legături externe
- Jerry Grossman, The Erdös Number Project. Contains statistics and a complete list of all mathematicians with an Erdős number less than or equal to 2.
- "On a Portion of the Well-Known Collaboration Graph", Jerrold W. Grossman and Patrick D. F. Ion.
- "Some Analyses of Erdős Collaboration Graph", Vladimir Batagelj and Andrej Mrvar.
- American Mathematical Society, MR Collaboration Distance. A search engine for Erdős numbers and collaboration distance between other authors. Special access required.
- "Theorems for Sale" (From Science News, Vol. 165, No. 24, June 12, 2004)
[modifică] Bibilografie
- Goffman, Casper (1969). „And What Is Your Erdös Number?”. American Mathematical Monthly 76 (7): 791. DOI:10.2307/2317868.
- De Castro, Rodrigo; Grossman, Jerrold W. (1999). „Famous Trails to Paul Erdős”. The Mathematical Intelligencer 21 (3): 51–63. MR1709679. Original Spanish version in Rev. Acad. Colombiana Cienc. Exact. Fís. Natur. 23 (89) 563–582, 1999, MR1744115.
