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 ...