Dr Fauzan Mirza | Assistant Professor | Department of Communication Systems Engineering


On this page, I will write about anything non-work related that I think is interesting, kind of like a blog.

Erdős number

An Erdös number of a person describes the maximum number of papers through which that person is linked, by a chain of co-authors, to the prolific mathematician Paul Erdös. For example, the following series of papers:

  1. S. R. Blackburn, K. Brincat, F. Mirza, and S. Murphy, “Cryptanalysis of ‘Labyrinth’ Stream Cipher”, IEE Electronics Letters, 38(12):1220-1221, 1998.
  2. X. Lai, J. L. Massey, and S. Murphy, “Markov Ciphers and Differential Cryptanalysis”, in Advances in Cryptology -- EUROCRYPT `91 , LNCS 547, pp. 17-38, Springer-Verlag, 1991.
  3. D. R. Stinson, J. L. Massey, “An Infinite Class of Counterexamples to a Conjecture Concerning Nonlinear Resilient Functions”, J. Cryptology, 8(3): 167-173, 1995.
  4. P. Erdös, R. C. Mullin, V. Sos, and D. R. Stinson, “Finite linear spaces and projective planes”, Discrete Math., 47:49-62, 1983.

Leads to the (first) following chain of co-authors, linking me to Paul Erdös:

  • Erdös-Stinson-Massey-Murphy-Mirza (Fauzan) [4]
  • Erdös-Cohen-Shparlinski-Blackburn-Mirza (Fauzan) [4]

In his lifetime, Paul Erdös published over 1500 papers and, as a result of having over 500 co-authors, many famous scientists, engineers and Nobel Prize laureates have a finite Erdös number, such as:

  • Erdös-Hell-Deng-Papadimitriou-Gates (Bill) [4] Founder and CEO of Microsoft
  • Erdös-Odlyzko-Skinner-Wiles (Andrew) [3] Prover of Fermat's Last Theorem
  • Erdös-Straus-Einstein (Albert) [2] Inventor of the theory of relativity, Nobel laureate (Physics)
  • Erdös-Chui-Ward-Salam (Abdus) [3] Pakistani Nobel laureate (Physics)
  • Erdös-Conway-Berlekamp-Shannon (Claude) [3] “Father of information theory”
  • Erdös-Holton-Hilton-Whitehead-Newman-Turing (Alan) [5] “Father of modern computer science”
  • Erdös-Darling-Taylor-Mandelbrot (Benoit) [3] “Father of fractal geometry”
  • Erdös-Niven-Schutzenberger-Chomsky (Noam) [3] Ideas of formal languages and grammers
  • Erdös-Odlyzko-Coppersmith (Don) [2] Inventor of Data Encryption Standard (DES) block cipher
  • Erdös-Linial-Rivest (Ron) [2] Inventor of RSA public-key cryptography and RC4/RC5 ciphers

Hence, through Paul Erdös and a chain of various co-authors, any person with a finite Erdös number is linked to everyone else with a finite Erdös number. So, for example, I am linked to Microsoft CEO Bill Gates by a list of 4+4=8 papers (at most) and to physicist Albert Einstein by a list of 4+2=6 papers (at most).

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Or is there? I'll add some more stuff here later. Maybe.