945 research outputs found
Restricted binary strings and generalized Fibonacci numbers
Part 2: Regular PapersInternational audienceWe provide some interesting relations involving k-generalized Fibonacci numbers between the set of length n binary strings avoiding k of consecutive 0’s and the set of length n strings avoiding consecutive 0’s and 1’s with some more restriction on the first and last letter, via a simple bijection. In the special case a probably new interpretation of Fibonacci numbers is given.Moreover, we describe in a combinatorial way the relation between the strings of with an odd numbers of 1’s and the ones with an even number of 1’s
Compositions, Bijections, and Enumerations
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
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 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
We deliver here second new recurrence formula,
were array is appointed by 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 coefficients onto
coefficients interpretations thus bringing us back to
and Donald Ervin Knuth relevant investigation decades
ago.Comment: 57 pages, 8 figure
- …