Shape and pattern containment of separable permutations. (Q2829071)

The authors assume that the terms used are known and use them to formulate the main result of the paper, which is given in Theorem 1, the statement of which is:NEWLINENEWLINE``If a word \(w\) contains a separable permutation \(\sigma\) as a pattern, then \(\mathrm{sh}(w)\!\supseteq\mathrm{sh}(\sigma)\)'',NEWLINENEWLINEwhere \(\mathrm{sh}(w)\) is the shape of the permutation \(w\), i.e. the sequence of lengths of the cycles in the representation of \(w\) as a product of disjoint cycles.NEWLINENEWLINEA word \(w\) is a supersequence of a set of permutation if, for all \(\sigma\) from this set, \(\sigma\) is a subsequence of \(w\). As an application of Theorem 1, the authors provide lower bounds for the lengths of supersequences of sets containing separable permutations.