Stacking sequence design of a composite laminate with a given set of plies is a combinatorial problem of seeking an optimal permutation. Permutation genetic algorithms optimizing the stacking sequence of a composite laminate for maximum buckling load are studied. A new permutation GA named gene±rank GA is developed and compared with an existing Partially Mapped Permutation GA, originally develo...

We study a group action on permutations due to Foata and Strehl and use it to prove that the descent generating polynomial of certain sets of permutations has a nonnegative expansion in the basis {t(1 + t)} i=0 , m = ⌊(n−1)/2⌋. This property implies symmetry and unimodality. We prove that the action is invariant under stack-sorting which strengthens recent unimodality results of Bóna. We prove ...

In this paper a new permutation generator is proposed. Each subsequent permutation is generated in a cellular permutation network by reversing a suffix/prefix of the preceding permutation. The sequence of suffix/prefix sizes is computed by a complex parallel counter in O(1) time per generated object. Suffix/prefix reversing operations are performed at the same time when the permutation is actua...

The technique of in-situ associative permuting is introduced which is an association of in-situ permuting and in-situ inverting. It is suitable for associatively permutable permutations of {1, 2, . . . , n} where the elements that will be inverted are negative and stored in order relative to each other according to their absolute values. Let K[1 . . . n] be an array of n integer keys each in th...

We introduce the class of permutation bigraphs as an analogue of permutation graphs. We show that this is precisely the class of bigraphs having Ferrers dimension at most 2. We also characterize the subclasses of interval bigraphs and indifference bigraphs in terms of their permutation labelings, and we relate permutation bigraphs to posets of dimension 2.

Two completely new algorithms for generating permutations–shift cursor algorithm and level algorithm–and their efficient implementations are presented in this paper. One implementation of shift cursor algorithm gives an optimal solution of permutation generation problem, and one implementation of level algorithm can be used to generate random permutations.

We give a recursive formula for the Möbius function of an interval [σ, π] in the poset of permutations ordered by pattern containment in the case where π is a decomposable permutation, that is, consists of two blocks where the first one contains all the letters 1, 2, . . . , k for some k. This leads to many special cases of more explicit formulas. It also gives rise to a computationally efficie...

We consider the problem of enumerating polynomials over Fq, that have certain coefficients prescribed to given values and permute certain substructures of Fq. In particular, we are interested in the group of N -th roots of unity and in the submodules of Fq. We employ the techniques of Konyagin and Pappalardi to obtain results that are similar to their results in [Finite Fields and their Applica...

P ∈ SN is a fast forward permutation if for each m the computational complexity of evaluating Pm(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in SN is (N) if one does not us...