The study of periodic musical structures leads to the computation of sequences satisfying some specific property in such a way that two solutions which are cyclic shifts of one another are considered the same. There exists a powerful technique to do so developed in combinatorics on words under the name of Lyndon words. We illustrate this by two examples taken from African traditional music.

We study the existence of periodic solutions of the non–autonomous periodic Lyness’ recurrence un+2 = (an +un+1)/un, where {an}n is a cycle with positive values a,b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5–periodic. We prove that for each pair (a, b) 6= (1, 1) there are infinitely many initial conditions giving ris...

The 2/1 resonant dynamics of a two-planet planar system is studied within the framework of the three-body problem by computing families of periodic orbits and their linear stability. The continuation of resonant periodic orbits from the restricted to the general problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular...

The paper investigates recoverability of sequences from their periodic subsequences and offers some modification of the approach suggested in papers arXiv:1605.00414and arXiv:1803.02233. It is shown that there exists a class of sequences that is everywhere dense in the class of all square-summable sequences and such that its members can be recovered from their periodic subsequences. This recove...

|Optimal sounding sequences which satisfy a certain autocorrelation property are useful for fast channel estimation techniques which are based on non-iterative channel sounding methods. In this paper, we study optimal sequences consisting of complex symbols with constant magnitude. An indirect sequence construction method is derived by considering the phase diierence between sequence symbols. O...

A method to generate a large number of M-ary Perfect Periodic Autocorrelation (PPAC) codes of length N, with good correlation properties, is presented. N+1 perfect sequences are obtained if an inverse discrete Fourier transform (IDFT) is applied to a specific subset of N+1 bipolar sequences derived from maximal-length sequences. This set of perfect sequences has a maximum absolute value of peri...

Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in Z only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretica...

This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any $n$ -tuple occurs at most once a period either direction. As has been previously described, such have potential applications automatic position-location systems, where the sequence...

In this paper, a constructive approach for determining CELCS (critical error linear complexity spectrum) for the kerror linear complexity distribution of 2-periodic binary sequences is developed via the sieve method and Games-Chan algorithm. Accordingly, the second descent point (critical point) distribution of the k-error linear complexity for 2-periodic binary sequences is characterized. As a...

A set of sequences is complementary, if the sum of their periodic or nonperiodic autocorrelation function is zero. Infinite families of orthogonal designs, based on some weighing matrices of order 2n, weight 2n− k and spread σ, are constructed from two circulants matrices by using complementary sequences of zero non-periodic autocorrelation function, i.e. ternary complementary pairs. Moreover, ...