Longest Common Separable Pattern between Permutations

Longest Common Pattern between two Permutations

In this paper, we give a polynomial (O(n)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the length of the longest simple permutation involved in one of our permutations.

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 Common Separable Pattern Among Permutations

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...

The 1-Box Pattern on Pattern-Avoiding Permutations

This paper is continuation of the study of the 1-box pattern in permutations introduced previously by the authors. We derive a two-variable generating function for the distribution of this pattern on 132-avoiding permutations, and then study some of its coefficients providing a link to the Fibonacci numbers. We also find the number of separable permutations with two and three occurrences of the...