Abstract Quantum permutations arise in many aspects of modern “quantum mathematics”. However, the aim this article is to detach these objects from their context and give a friendly introduction purely within operator theory. We define quantum permutation matrices as whose entries are operators on Hilbert spaces; they obey certain assumptions generalizing classical matrices. number examples we l...

Four recursive constructions of permutation polynomials over GF(q2) with those over GF(q) are developed and applied to a few famous classes of permutation polynomials. They produce infinitely many new permutation polynomials over GF(q2 l ) for any positive integer l with any given permutation polynomial over GF(q). A generic construction of permutation polynomials over GF(22m) with o-polynomial...

A permutation is called simple if its only blocks i.e. subsets of the permutation consist of singleton and the permutation itself. For example, 2134 is not a simple permutation since it consists of a block 213 but 3142 is a simple permutation. The basis of a permutation is a pattern which is minimal under involvement and do not belong to the permutation. In this paper, we prove that the number ...

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...

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.