Longest Common Pattern between two Permutations

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 longes...

The Longest Common Pattern Problem for two Permutations

The study of patterns in permutations has blossomed these last years: from a combinatorial point of view with the recent proof of the Stanley–Wilf conjecture by Marcus and Tardös, and from an algorithmic one with the development of algorithms for pattern involvement. Although the general pattern involvement problem is NP -hard, some polynomial solutions exist for special kinds of patterns like ...

Longest Alternating Subsequences in Pattern-Restricted Permutations

Inspired by the results of Stanley and Widom concerning the limiting distribution of the lengths of longest alternating subsequences in random permutations, and results of Deutsch, Hildebrand and Wilf on the limiting distribution of the longest increasing subsequence for pattern-restricted permutations, we find the limiting distribution of the longest alternating subsequence for pattern-restric...

Longest Common Separable Pattern Among Permutations

Longest Monotone Subsequences and Rare Regions of Pattern-Avoiding Permutations

We consider the distributions of the lengths of the longest monotone and alternating subsequences in classes of permutations of size n that avoid a specific pattern or set of patterns, with respect to the uniform distribution on each such class. We obtain exact results for any class that avoids two patterns of length 3, as well as results for some classes that avoid one pattern of length 4 or m...