4 research outputs found

    Restricted binary strings and generalized Fibonacci numbers

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    Part 2: Regular PapersInternational audienceWe provide some interesting relations involving k-generalized Fibonacci numbers between the set Fn(k)F_n^{(k)} of length n binary strings avoiding k of consecutive 0’s and the set of length n strings avoiding k+1k+1 consecutive 0’s and 1’s with some more restriction on the first and last letter, via a simple bijection. In the special case k=2k=2 a probably new interpretation of Fibonacci numbers is given.Moreover, we describe in a combinatorial way the relation between the strings of Fn(k)F_n^{(k)} with an odd numbers of 1’s and the ones with an even number of 1’s

    A gray code for a regular language

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