====== Erdős Number ======

In the world of mathematics, you can see networking effects in terms of your //Erdős number// which quantifies the series of connections through the scientific community to the published work of [[wp>Paul Erdős]]. As well as being a prolific author of mathematical papers, [[wp>Paul Erdős]] was also quite an enigmatic character. His biography, [[wp>The Man Who Loved Only Numbers]], is worth a read.

To be assigned an Erdős number, one must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is $k + 1$ where $k$ is the lowest Erdős number of any co-author.

Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators; 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 (9267 people as of 2010), 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 an Erdős number of infinity (or an undefined one). Since the death of Paul Erdős, the lowest Erdős number that a researcher can obtain is 2. ((http://en.wikipedia.org/wiki/Erd%C5%91s_number))

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Below is the distribution of Erdős Numbers((http://www.oakland.edu/enp/trivia/))
   Erdös number  0  ---      1 person  
      Erdös number  1  ---    504 people
      Erdös number  2  ---   6593 people
      Erdös number  3  ---  33605 people
      Erdös number  4  ---  83642 people
      Erdös number  5  ---  87760 people
      Erdös number  6  ---  40014 people
      Erdös number  7  ---  11591 people
      Erdös number  8  ---   3146 people
      Erdös number  9  ---    819 people
      Erdös number 10  ---    244 people
      Erdös number 11  ---     68 people
      Erdös number 12  ---     23 people
      Erdös number 13  ---      5 people


====== My Erdős Number would appear to be 5 ======


==== Erdős Number 5 ====

Checking through AMS:\\
http://www.ams.org/mathscinet/collaborationDistance.html




=== Path 1 ===

O'Brien-Huyet/McInerney-**Pokrovskii**-Boltyanskii-Soifer-Erdős

//"Rigorous analysis of complicated behaviour in a truncated LangKobayashi model"//  
O. Rasskazov, G. Huyet, J. Mcinerney, **A. Pokrovskii**\\
  * **Alexei V. Pokrovskii**  coauthored with  Vladimir Grigorʹevich Boltyanskii  MR0862446 (88a:93001)  
  * Vladimir Grigorʹevich Boltyanskii  coauthored with  Alexander Soifer  MR1104655 (92f:52031)  
  * Alexander Soifer  coauthored with  Paul Erdős1  MR1214695  

=== Path 2 ===
Stephen Barnett is same or??
Huyet-Barnett-Johnson-Schönheim-Erdős \\
//Superposition states at finite temperature//
G. Huyet, S Franke-Arnold, **S.M. Barnett** 
 

  * **Stephen Barnett ** coauthored with  Charles R. Johnson  MR0943760 (89c:15005)  
  * Charles R. Johnson  coauthored with  Johanan Schönheim  MR0705965 (84j:15007)  
  * Johanan Schönheim  coauthored with  Paul Erdős1  




=== Path 3 ===

Arlazarov, V. L.; **Uskov, A. V.** Faradžev, I. A. //An algorithm for finding all simple cycles in a directed graph. (Russian)  Studies in discrete mathematics (Russian)//,  pp. 178–183. Izdat."Nauka'', Moscow, 1973. 

MR Erdos Number = 4 
  * **A. V. Uskov ** coauthored with  I. A. Faradzhev  MR0412019 (54 #148)  
  * I. A. Faradzhev  coauthored with  Mikhail H. Klin  MR0617203 (82g:20012)  
  * Mikhail H. Klin  coauthored with  Peter J. Cameron  MR1920405 (2003f:20001)  
  * Peter J. Cameron  coauthored with  Paul Erdős1  MR1106651 (92g:11010)  




=== Path 4 ===

MR2070618 34C23 (34C25 34K13 34K18)
Krasnoselʹskii, A. M.; McInerney, J.; Pokrovskii, A. V. Synchronized double-frequency oscillations in a class of weakly resonant systems. Nonlinear Anal. 57 (2004), no. 7-8, 929–949. 

MR Erdos Number = 4
  * J. G. McInerney 	coauthored with 	Alexander M. Krasnoselʹskii 	MR2070618
  * Alexander M. Krasnoselʹskii 	coauthored with 	Vladimir Grigorʹevich Boltyanskii 	MR0862446
  * Vladimir Grigorʹevich Boltyanskii 	coauthored with 	Alexander Soifer 	MR1104655
  * Alexander Soifer 	coauthored with 	Paul Erdős1 	MR1214695

==== Erdős Number 4 ? ====
tool From [[http://academic.research.microsoft.com/VisualExplorer#416632&1112639
|Microsoft]] would suggest Erdös number of 4 
McInerney-H.S.Gamble-H.L.Montogmery-Erdős

doesn't look reliable though, results don't make sense.. (McInerney search does not show this link!)


~~DISCUSSION~~