This paper deals with the amount of disorder that is left in a permutation after one of its elements has been selected with quickselect with or without median-of-three pivoting. Five measures of disorder are considered: inversions, cycles of length less than or equal to some m, cycles of any length, expected cycle length, and the distance to the identity permutation. “Grand averages” for each m...

We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of points to its left. We use this characterisation to establish the generating function enumerating these permutations. We also investigate the properties of a...

This paper presents a bit level pixel by pixel chaotic image encryption scheme with a permutation–diffusion structure. In this scheme, a Neural Network Like Structure (NNLS) is proposed to do the diffusion efficiently. The plain image, split into 16 blocks is permuted by the keys from the key generator. Each key will produce different permutation order (PO) generated using a chaotic map. After ...

In this work we introduce and study a set of new interleavers based on permutation polynomials and functions with known inverses over a finite field Fq for using in turbo code structures. We use Monomial, Dickson, Möbius and Rédei functions in order to get new interleavers. In addition we employ Skolem sequences in order to find new interleavers with known cycle structure. As a byproduct we giv...

We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length. Second, on this basis, we give an elementary alternative proof of the equality between the permutation entropy rate and ...

The permutation representation theory of groups has been extended, through quasigroups, to one-sided left (or right) quasigroups. The current paper establishes a link with the theory of ordered sets, introducing the concept of a Burnside order that generalizes the poset of conjugacy classes of subgroups of a finite group. Use of the Burnside order leads to a simplification in the proof of key p...

A generic matrix A ∈ Cn×n is shown to be the product of circulant and diagonal matrices with the number of factors being 2n−1 at most. The demonstration is constructive, relying on first factoring matrix subspaces equivalent to polynomials in a permutation matrix over diagonal matrices into linear factors. For the linear factors, the sum of two scaled permutations is factored into the product o...

This paper reviews some possible design criteria for the permutation P in a DES style cryptosystem. These permutations provide the diffusion component in a substitution-permutation network. Some empirical rules which seem to account for the derivation of the permutation used in the DES are first presented. Then it is noted that these permutations may be regarded as latin-squares which link the ...

A permutation group on a countably infinite domain is called oligomorphic if it has finitely many orbits of finitary tuples. We define a clone on a countable domain to be oligomorphic if its set of permutations forms an oligomorphic permutation group. There is a close relationship to ω-categorical structures, i.e., countably infinite structures with a firstorder theory that has only one countab...

What governs the balance between connectivity and topology in regulating the mechanism of protein folding? We use circular permutation to vary the order of the helices in the all-α Greek key protein FADD (Fas-associated death domain) to investigate this question. Unlike all-β Greek key proteins, where changes in the order of secondary structure cause a shift in the folding nucleus, the position...