Beggas, F.; Ferrari, M. M.; Kheddouci, H.; Salvi, N. Zagaglia On circular disarranged strings of sequences. (English) Zbl 1357.05002 Adv. Appl. Discrete Math. 17, No. 3, 275-292 (2016). Summary: Two sequences \((a_1,a_2,\ldots,a_n)\) and \((b_1,b_2,\ldots,b_n)\) sharing \(n-1\) elements, are said disarranged if for every non-empty subset \(Q \subseteq [n]\), the sets \(\{a_i\mid i\in Q\}\) and \(\{b_i\mid i \in Q\}\) are different. In this paper we investigate properties of these pairs of sequences. Moreover, we extend the definition of disarranged pairs to a circular string of \(n\)-sequences and prove that, for every positive integer \(m\), except some initials values for \(n\) even, there exists a similar structure of length \(m\). MSC: 05A05 Permutations, words, matrices 05C15 Coloring of graphs and hypergraphs Keywords:direct product of graphs; adjacent vertex distinguishing chromatic index; cyclic permutation; derangement; disarranged sequences; 1-disarranged sequences; circular disarranged string PDFBibTeX XMLCite \textit{F. Beggas} et al., Adv. Appl. Discrete Math. 17, No. 3, 275--292 (2016; Zbl 1357.05002) Full Text: DOI Link