Lexicographic permutations with restrictions

Multiset Permutations in Lexicographic Order

In a previous work [12], we proposed a method for generating permutations in lexicographic order. In this study, we extend it to generate multiset permutations. A multiset is a collection of items that are not necessarily distinct. The guideline of the extension is to skip, as soon as possible, those partially-formed permutations that are less than or equal to the latest generated eligible perm...

Alternating Permutations with Restrictions and Standard Young Tableaux

Abstract. In this paper, we establish bijections between the set of 4123-avoiding In this paper, we establish bijections between the set of 4123-avoiding down-up alternating permutations of length 2n and the set of standard Young tableaux of shape (n, n, n), and between the set of 4123-avoiding down-up alternating permutations of length 2n−1 and the set of shifted standard Young tableaux of sha...

A New Method for Generating Permutations in Lexicographic Order

First, an ordinal representation scheme for permutations is defined. Next, an “unranking” algorithm that can generate a permutation of n items according to its ordinal representation is designed. By using this algorithm, all permutations can be systematically generated in lexicographic order. Finally, a “ranking” algorithm that can convert a permutation to its ordinal representation is designed...

Efficient Algorithms to Rank and Unrank Permutations in Lexicographic Order

We present uniform and non-uniform algorithms to rank and unrank permutations in lexicographic order. The uniform algorithms run in O(n log n) time and outperform Knuth’s ranking algorithm in all the experiments, and also the lineartime non-lexicographic algorithm of Myrvold-Ruskey for permutations up to size 128. The non-uniform algorithms generalize Korf-Schultze’s linear time algorithm yet r...

An Optimal Systolic Algorithm for Generating Permutations in Lexicographic Order