6,297 research outputs found
Longest Common Separable Pattern between Permutations
In this article, we study the problem of finding the longest common separable
pattern between several permutations. We give a polynomial-time algorithm when
the number of input permutations is fixed and show that the problem is NP-hard
for an arbitrary number of input permutations even if these permutations are
separable. On the other hand, we show that the NP-hard problem of finding the
longest common pattern between two permutations cannot be approximated better
than within a ratio of (where is the size of an optimal
solution) when taking common patterns belonging to pattern-avoiding classes of
permutations.Comment: 15 page
A simple and unusual bijection for Dyck paths and its consequences
In this paper we introduce a new bijection from the set of Dyck paths to
itself. This bijection has the property that it maps statistics that appeared
recently in the study of pattern-avoiding permutations into classical
statistics on Dyck paths, whose distribution is easy to obtain.
We also present a generalization of the bijection, as well as several
applications of it to enumeration problems of statistics in restricted
permutations.Comment: 13 pages, 8 figures, submitted to Annals of Combinatoric
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