×

On circular disarranged strings  of sequences. (English) Zbl 1357.05002

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
PDFBibTeX XMLCite
Full Text: DOI Link