06 March 2009

One of my favorite bad math jokes ever is now in Wikipedia, and no, I didn't add it.

Namely, exercise 6.24 of Richard Stanley's Enumerative Combinatorics, Volume 2 asks the reader to

"Explain the significance of the following sequence: un, dos, tres, quatre, cinc, sis, set, vuit, nou, deu..."

The answer is that these are the "Catalan numbers", i. e. the numbers in the Catalan language. If this seems random, note that exercise 6.21 is the famous exercise in 66 parts (169 in the extended online version, labelled (a) through (m7)), which asks the reader to prove that 66 (or 169) different sets are counted by the Catalan numbers.

I'm telling you about this joke because the Wikipedia article on Catalan numbers begins with a link to the list of numbers in various languages.

An alternative version of this joke (American Mathematical Monthly, vol. 103 (1996), pages 538 and 577) asks you to identify the sequence "una, dues, cinc, catorze, quaranta-dues, cent trenta-dues, quatre-cent vint-i-nou,...", which are the Catalan numbers 1, 2, 5, 14, 42, 132, 429... in the Catalan language. (I'm reporting the spellings as I found them in my sources; the first series is in the masculine and the second is in the feminine, as Juan Miguel pointed out in the comments.)

1 comment:

Juan Miguel Vilar said...

I wouldn't like to apper pedantic, but the spelling of numbers in the Catalan language is standardized: the difference between the two series comes from the first being in the masculine and the second in the feminine.

Regards,

Juan Miguel