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...