De Bruijn Sequence

see sequence, substring, set, math notation

definition a De Bruijn sequence of order n on a finite alphabet A is a cyclic sequence in which every possible length-n string on A occurs exactly once as a substring --- GitHub Copilot

notation

the set of all de bruijn sequences of order n on A

B^n A

properties

# (B^n A) = [# A]n

examples

• B^3 {{''0'', ''1''}} ""00010111""
• B^4 {{''0'', ''1''}} ""0000100110101111""
• B^5 {{''0'', ''1''}} ""00000100011001010011101011011111""

--- https://en.wikipedia.org/wiki/De_Bruijn_sequence

applications

opening garage doors --- https://youtu.be/CNodxp9Jy4A