[seqfan] Re: Who named Catalan numbers?

Peter Luschny peter.luschny at gmail.com
Sat Feb 8 13:04:01 CET 2014

HWG> In my work over the past 60 years I have sometimes
HWG> called the numbers 1, 2, 2, 5, 14, 42, ... the
HWG> 'Euler-Fuss-Segner-Catalan' numbers, especially in
HWG> my well-known Bibilography. But I always agreed with
HWG> my old friends John Riordan and Leonard Carlitz that
HWG> the single name 'Catalan' was sufficient unto the
HWG> purpose thereof.

Maybe even better then 'Euler-Fuss-Segner-Catalan' would
be 'Euler-Fuss-Segner-Lamé'. It was Gabriel Lamé who
proved Euler's conjecture P_{n+1}=P_{n}(4n-6)/n in 1838.
Thus the most important relations of the Catalan numbers
were investigated and proved before Catalan entered the scene.

(See page 19 of this nice talk on the history of Catalan numbers
which shows a paper of Catalan deriving some consequences
from Lamé's proof:
http://www.mathnet.or.kr/real/2010/01/OtfriedCheong(0112).pdf )

HWG> but the appellation 'Cauchy-Schwartz-Bouniakovsky Inequality'
HWG> is rather a mouthful to keep saying and so in his lectures he
HWG> sometimes just called it 'inequality 3.19'.

Certainly 'Cauchy-Schwartz' is better than 'inequality 3.19' as
'Catalan numbers' is better than 'A000108'.

On the other hand the name 'Euler-Lamé' seems to me both
historical appropriate and short enough to use in a lecture.


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