### Table of Contents

# 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 Paul Erdős. As well as being a prolific author of mathematical papers, Paul Erdős was also quite an enigmatic character. His biography, 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. ^{1)}

Below is the distribution of Erdős Numbers^{2)}

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 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~~

^{1)}