De Bruijn sequences

Panel 1: The mathematician: You know what would be neat? Changing your name to a de Bruijn sequence. Then you'd have this really long name, but you could claim that any substring was a valid nickname. Panel 2: Man: How would you manage that? In order to generate a string containing all 4-letter substrings of a 26 letter alphabet you need 26^4 characters. That's really long. Panel 3: The mathematician: Okay, I'd just name myself ttmmtmmmmammhamhaahatahamatamahahaattaatmaathtathmathhatmtatmmatmhatttattmatthathamttamtmttttmtmamamthaaatataaamaaaahtaahmaahhtahhmahhhthhhmtthmthhmmmhmtmhmmhhmhthmhhhahmtahmmthmmahmhmhahttahtmthtmmhttthttmhtmhhtthhtmahththahhaamtaammaamhtamhmamhhammtammm. (The other 22 letters aren't that important) Panel 4: The mathematician: See? Now I can be nicknamed math, matt, hat, that, or ham. Man: How do you plan on dealing with the fact that de Bruijn sequences aren't unique? The mathematician: Be quiet.

Is it possible to make your name the empty set?

De Bruijn sequences

24 January 2007