Generalized Fibonacci recurrences and the lex-least De Bruijn sequence
نویسندگان
چکیده
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 lexicographicallyleast 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.
منابع مشابه
The discrepancy of the lex-least de Bruijn sequence
We answer the following question of R. L. Graham: What is the discrepancy of the lexicographically-least binary de Bruijn sequence? Here, “discrepancy” refers to the maximum (absolute) difference between the number of ones and the number of zeros in any initial segment of the sequence. We show that the answer is Θ(2 log n/n).
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