Smooth words are in nite words connected with the one de ned by Kolakoski. This class is obtained by a bijective map on the free monoid over = f1; 2g that shows some surprising mixing properties andâ€¦ (More)

The discrete version of Greenâ€™s Theorem and bivariate difference calculus provide a general and unifying framework for the description and generation of incremental algorithms. It may be used toâ€¦ (More)

We give explicit formulas for the number Un(N) of closed polygonal paths of length N (starting from the origin) whose steps are n roots of unity, as well as asymptotic expressions for these numbersâ€¦ (More)

By using the discrete version of Greenâ€™s theorem and bivariate difference calculus we provide incremental algorithms to compute various statistics about polyominoes given, as input, by 4-letter wordsâ€¦ (More)

We consider the shuffle operation on paths and study some parameters. In the case of square lattices, shuffling with a particular periodic word (of period 2) corresponding to paperfoldings revealsâ€¦ (More)

We analyze the moment of inertia I(S), relative to the center of gravity, of finite plane lattice sets S. We classify these sets according to their roundness: a set S is rounder than a set T if I(S)â€¦ (More)

The construction of a Sturmian word, and thus of a discrete line, from a continued fraction development generalizes to higher dimension. Given any vector v âˆˆ R, a list of 6-connected pointsâ€¦ (More)