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...

This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank $23$ decompositions for the $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and...

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 ...

We present a bijection between cyclic permutations of {1, 2, . . . , n+1} and permutations of {1, 2, . . . , n} that preserves the descent set of the first n entries and the set of weak excedances. This non-trivial bijection involves a Foata-like transformation on the cyclic notation of the permutation, followed by certain conjugations. We also give an alternate derivation of the consequent res...

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...

This paper describes saturation attacks on reduced-round versions of Skipjack. To begin with, we will show how to construct a 16-round distinguisher which distinguishes 16 rounds of Skipjack from a random permutation. The distinguisher is used to attack on 18(5∼22) and 23(5∼27) rounds of Skipjack. We can also construct a 20-round distinguisher based on the 16-round distinguisher. This distingui...

Three papers in the Journal this month examine the impact on service use of particular service developments and patient/illness characteristics. Williams et al (pp. 480–485) compared patterns of service use, including hospital admission rates, before and after the introduction of a triage admission system in one large innercity mental health organisation. Overall, little difference was found be...