Norma Zagaglia Salvi

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The Fibonacci cube n is the graph whose vertices are binary strings of length n without two consecutive 1’s and two vertices are adjacent when their Hamming distance is exactly 1. If the binary strings do not contain two consecutive 1’s nor a 1 in the 7rst and in the last position, we obtain the Lucas cube Ln. We prove that the observability of n and Ln is(More)
A Fibonacci string of order n is a binary string of length n with no two consecutive ones. The Fibonacci cube n is the subgraph of the hypercube Qn induced by the set of Fibonacci strings of order n. For positive integers i; n, with n¿ i, the ith extended Fibonacci cube is the vertex induced subgraph of Qn for which V ( i n) = V i n is de2ned recursively by(More)
We study several enumerative properties of the set of all binary strings without zigzags, i.e., without substrings equal to 101 or 010 . Specifically we give the generating series, a recurrence and two explicit formulas for the number wm,n of these strings with m 1’s and n 0’s and in particular for the numbers wn = wn,n of central strings. We also consider(More)
We study combinatorial properties of the species of scattered subsets in the case of linearly ordered sets and in the case of cycles. In particular, we study the numbers of such subsets which turn out to be a generalization of Fibonacci and Lucas numbers. We also determine a generalization of the Cassini’s identity. Finally, we de3ne a q-analog of such(More)