945 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

    Compositions, Bijections, and Enumerations

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    In this thesis we give an introduction to colored-compositions of an integer. This is a generalization of traditional integer compositions, and we show a few results for n-color compositions which are analogous to regular compositions with both combinatorial and analytic proofs. We also show several bijections between various types of compositions to certain types of numeric strings, and provide a generalization of a classic bijection between compositions and binary strings

    Real-Time Vector Automata

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    We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected k×kk \times k matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and "blind" versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.Comment: 14 page

    Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II

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    We deliver here second new H(x)−binomials′\textit{H(x)}-binomials' recurrence formula, were H(x)−binomials′H(x)-binomials' array is appointed by Ward−HoradamWard-Horadam sequence of functions which in predominantly considered cases where chosen to be polynomials . Secondly, we supply a review of selected related combinatorial interpretations of generalized binomial coefficients. We then propose also a kind of transfer of interpretation of p,q−binomialp,q-binomial coefficients onto q−binomialq-binomial coefficients interpretations thus bringing us back to Gyo¨rgyPoˊlyaGy{\"{o}}rgy P\'olya and Donald Ervin Knuth relevant investigation decades ago.Comment: 57 pages, 8 figure

    Robust Transmission of Unbounded Strings Using Fibonacci Representations

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