Generalized Fibonacci recurrences and the lex-least De Bruijn sequence

Details Generalized Fibonacci recurrences and the lex-least De Bruijn sequence Generalized Fibonacci recurrences and the lex-least De Bruijn sequence

2010-03-30

arxiv.org/abs/1003.5939v1

Mathematics

Combinatorics

10 pages, 1 figure, 2 tables

Scientific paper

The skew of a binary string is the difference between the number of zeroes and the number of ones, while the length of the string is the sum of these two numbers. We consider certain suffixes of the lexicographically-least de Bruijn sequence at natural breakpoints of the binary string. We show that the skew and length of these suffixes are enumerated by sequences generalizing the Fibonacci and Lucas numbers, respectively.

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